Pre-Algebra Examples

$\begin{array}{c} x & y \\ 0 & 9 \\ 5 & 7 \\ 6 & 7 \\ 9 & 6 \\ 13 & 9 \\ 16 & 7 \\ 19 & 8 \\ 22 & 6 \end{array}$

Step 1

Check if the function rule is linear.

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Step 1.1

To find if the table follows a function rule, check to see if the values follow the linear form $y = a x + b$ .

$y = a x + b$

Step 1.2

Build a set of equations from the table such that $y = a x + b$ .

$9 = a (0) + b 7 = a (5) + b 7 = a (6) + b 6 = a (9) + b 9 = a (13) + b 7 = a (16) + b 8 = a (19) + b 6 = a (22) + b$

Step 1.3

Calculate the values of $a$ and $b$ .

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Step 1.3.1

Rewrite the equation as $b = 9$ .

$b = 9$

$7 = a (5) + b$

$7 = a (6) + b$

$6 = a (9) + b$

$9 = a (13) + b$

$7 = a (16) + b$

$8 = a (19) + b$

$6 = a (22) + b$

Step 1.3.2

Replace all occurrences of $b$ with $9$ in each equation.

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Step 1.3.2.1

Replace all occurrences of $b$ in $7 = a (5) + b$ with $9$ .

$7 = a (5) + 9$

$b = 9$

$7 = a (6) + b$

$6 = a (9) + b$

$9 = a (13) + b$

$7 = a (16) + b$

$8 = a (19) + b$

$6 = a (22) + b$

Step 1.3.2.2

Simplify $7 = a (5) + 9$ .

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Step 1.3.2.2.1

Simplify the left side.

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Step 1.3.2.2.1.1

Remove parentheses.

$7 = a (5) + 9$

$b = 9$

$7 = a (6) + b$

$6 = a (9) + b$

$9 = a (13) + b$

$7 = a (16) + b$

$8 = a (19) + b$

$6 = a (22) + b$

$7 = a (5) + 9$

$b = 9$

$7 = a (6) + b$

$6 = a (9) + b$

$9 = a (13) + b$

$7 = a (16) + b$

$8 = a (19) + b$

$6 = a (22) + b$

Step 1.3.2.2.2

Simplify the right side.

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Step 1.3.2.2.2.1

Move $5$ to the left of $a$ .

$7 = 5 a + 9$

$b = 9$

$7 = a (6) + b$

$6 = a (9) + b$

$9 = a (13) + b$

$7 = a (16) + b$

$8 = a (19) + b$

$6 = a (22) + b$

$7 = 5 a + 9$

$b = 9$

$7 = a (6) + b$

$6 = a (9) + b$

$9 = a (13) + b$

$7 = a (16) + b$

$8 = a (19) + b$

$6 = a (22) + b$

$7 = 5 a + 9$

$b = 9$

$7 = a (6) + b$

$6 = a (9) + b$

$9 = a (13) + b$

$7 = a (16) + b$

$8 = a (19) + b$

$6 = a (22) + b$

Step 1.3.2.3

Replace all occurrences of $b$ in $7 = a (6) + b$ with $9$ .

$7 = a (6) + 9$

$7 = 5 a + 9$

$b = 9$

$6 = a (9) + b$

$9 = a (13) + b$

$7 = a (16) + b$

$8 = a (19) + b$

$6 = a (22) + b$

Step 1.3.2.4

Simplify $7 = a (6) + 9$ .

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Step 1.3.2.4.1

Simplify the left side.

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Step 1.3.2.4.1.1

Remove parentheses.

$7 = a (6) + 9$

$7 = 5 a + 9$

$b = 9$

$6 = a (9) + b$

$9 = a (13) + b$

$7 = a (16) + b$

$8 = a (19) + b$

$6 = a (22) + b$

$7 = a (6) + 9$

$7 = 5 a + 9$

$b = 9$

$6 = a (9) + b$

$9 = a (13) + b$

$7 = a (16) + b$

$8 = a (19) + b$

$6 = a (22) + b$

Step 1.3.2.4.2

Simplify the right side.

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Step 1.3.2.4.2.1

Move $6$ to the left of $a$ .

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$6 = a (9) + b$

$9 = a (13) + b$

$7 = a (16) + b$

$8 = a (19) + b$

$6 = a (22) + b$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$6 = a (9) + b$

$9 = a (13) + b$

$7 = a (16) + b$

$8 = a (19) + b$

$6 = a (22) + b$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$6 = a (9) + b$

$9 = a (13) + b$

$7 = a (16) + b$

$8 = a (19) + b$

$6 = a (22) + b$

Step 1.3.2.5

Replace all occurrences of $b$ in $6 = a (9) + b$ with $9$ .

$6 = a (9) + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$9 = a (13) + b$

$7 = a (16) + b$

$8 = a (19) + b$

$6 = a (22) + b$

Step 1.3.2.6

Simplify $6 = a (9) + 9$ .

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Step 1.3.2.6.1

Simplify the left side.

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Step 1.3.2.6.1.1

Remove parentheses.

$6 = a (9) + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$9 = a (13) + b$

$7 = a (16) + b$

$8 = a (19) + b$

$6 = a (22) + b$

$6 = a (9) + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$9 = a (13) + b$

$7 = a (16) + b$

$8 = a (19) + b$

$6 = a (22) + b$

Step 1.3.2.6.2

Simplify the right side.

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Step 1.3.2.6.2.1

Move $9$ to the left of $a$ .

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$9 = a (13) + b$

$7 = a (16) + b$

$8 = a (19) + b$

$6 = a (22) + b$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$9 = a (13) + b$

$7 = a (16) + b$

$8 = a (19) + b$

$6 = a (22) + b$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$9 = a (13) + b$

$7 = a (16) + b$

$8 = a (19) + b$

$6 = a (22) + b$

Step 1.3.2.7

Replace all occurrences of $b$ in $9 = a (13) + b$ with $9$ .

$9 = a (13) + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$7 = a (16) + b$

$8 = a (19) + b$

$6 = a (22) + b$

Step 1.3.2.8

Simplify $9 = a (13) + 9$ .

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Step 1.3.2.8.1

Simplify the left side.

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Step 1.3.2.8.1.1

Remove parentheses.

$9 = a (13) + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$7 = a (16) + b$

$8 = a (19) + b$

$6 = a (22) + b$

$9 = a (13) + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$7 = a (16) + b$

$8 = a (19) + b$

$6 = a (22) + b$

Step 1.3.2.8.2

Simplify the right side.

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Step 1.3.2.8.2.1

Move $13$ to the left of $a$ .

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$7 = a (16) + b$

$8 = a (19) + b$

$6 = a (22) + b$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$7 = a (16) + b$

$8 = a (19) + b$

$6 = a (22) + b$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$7 = a (16) + b$

$8 = a (19) + b$

$6 = a (22) + b$

Step 1.3.2.9

Replace all occurrences of $b$ in $7 = a (16) + b$ with $9$ .

$7 = a (16) + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$8 = a (19) + b$

$6 = a (22) + b$

Step 1.3.2.10

Simplify $7 = a (16) + 9$ .

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Step 1.3.2.10.1

Simplify the left side.

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Step 1.3.2.10.1.1

Remove parentheses.

$7 = a (16) + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$8 = a (19) + b$

$6 = a (22) + b$

$7 = a (16) + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$8 = a (19) + b$

$6 = a (22) + b$

Step 1.3.2.10.2

Simplify the right side.

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Step 1.3.2.10.2.1

Move $16$ to the left of $a$ .

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$8 = a (19) + b$

$6 = a (22) + b$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$8 = a (19) + b$

$6 = a (22) + b$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$8 = a (19) + b$

$6 = a (22) + b$

Step 1.3.2.11

Replace all occurrences of $b$ in $8 = a (19) + b$ with $9$ .

$8 = a (19) + 9$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$6 = a (22) + b$

Step 1.3.2.12

Simplify $8 = a (19) + 9$ .

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Step 1.3.2.12.1

Simplify the left side.

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Step 1.3.2.12.1.1

Remove parentheses.

$8 = a (19) + 9$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$6 = a (22) + b$

$8 = a (19) + 9$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$6 = a (22) + b$

Step 1.3.2.12.2

Simplify the right side.

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Step 1.3.2.12.2.1

Move $19$ to the left of $a$ .

$8 = 19 a + 9$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$6 = a (22) + b$

$8 = 19 a + 9$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$6 = a (22) + b$

$8 = 19 a + 9$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$6 = a (22) + b$

Step 1.3.2.13

Replace all occurrences of $b$ in $6 = a (22) + b$ with $9$ .

$6 = a (22) + 9$

$8 = 19 a + 9$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.2.14

Simplify $6 = a (22) + 9$ .

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Step 1.3.2.14.1

Simplify the left side.

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Step 1.3.2.14.1.1

Remove parentheses.

$6 = a (22) + 9$

$8 = 19 a + 9$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$6 = a (22) + 9$

$8 = 19 a + 9$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.2.14.2

Simplify the right side.

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Step 1.3.2.14.2.1

Move $22$ to the left of $a$ .

$6 = 22 a + 9$

$8 = 19 a + 9$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$6 = 22 a + 9$

$8 = 19 a + 9$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$6 = 22 a + 9$

$8 = 19 a + 9$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$6 = 22 a + 9$

$8 = 19 a + 9$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.3

Solve for $a$ in $6 = 22 a + 9$ .

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Step 1.3.3.1

Rewrite the equation as $22 a + 9 = 6$ .

$22 a + 9 = 6$

$8 = 19 a + 9$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.3.2

Move all terms not containing $a$ to the right side of the equation.

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Step 1.3.3.2.1

Subtract $9$ from both sides of the equation.

$22 a = 6 - 9$

$8 = 19 a + 9$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.3.2.2

Subtract $9$ from $6$ .

$22 a = - 3$

$8 = 19 a + 9$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$22 a = - 3$

$8 = 19 a + 9$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.3.3

Divide each term in $22 a = - 3$ by $22$ and simplify.

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Step 1.3.3.3.1

Divide each term in $22 a = - 3$ by $22$ .

$\frac{22 a}{22} = \frac{- 3}{22}$

$8 = 19 a + 9$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.3.3.2

Simplify the left side.

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Step 1.3.3.3.2.1

Cancel the common factor of $22$ .

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Step 1.3.3.3.2.1.1

Cancel the common factor.

$\frac{22 a}{22} = \frac{- 3}{22}$

$8 = 19 a + 9$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.3.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 3}{22}$

$8 = 19 a + 9$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$a = \frac{- 3}{22}$

$8 = 19 a + 9$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$a = \frac{- 3}{22}$

$8 = 19 a + 9$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.3.3.3

Simplify the right side.

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Step 1.3.3.3.3.1

Move the negative in front of the fraction.

$a = - \frac{3}{22}$

$8 = 19 a + 9$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$a = - \frac{3}{22}$

$8 = 19 a + 9$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$a = - \frac{3}{22}$

$8 = 19 a + 9$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$a = - \frac{3}{22}$

$8 = 19 a + 9$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4

Replace all occurrences of $a$ with $- \frac{3}{22}$ in each equation.

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Step 1.3.4.1

Replace all occurrences of $a$ in $8 = 19 a + 9$ with $- \frac{3}{22}$ .

$8 = 19 (- \frac{3}{22}) + 9$

$a = - \frac{3}{22}$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.2

Simplify the right side.

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Step 1.3.4.2.1

Simplify $19 (- \frac{3}{22}) + 9$ .

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Step 1.3.4.2.1.1

Simplify each term.

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Step 1.3.4.2.1.1.1

Multiply $19 (- \frac{3}{22})$ .

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Step 1.3.4.2.1.1.1.1

Multiply $- 1$ by $19$ .

$8 = - 19 (\frac{3}{22}) + 9$

$a = - \frac{3}{22}$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.2.1.1.1.2

Combine $- 19$ and $\frac{3}{22}$ .

$8 = \frac{- 19 \cdot 3}{22} + 9$

$a = - \frac{3}{22}$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.2.1.1.1.3

Multiply $- 19$ by $3$ .

$8 = \frac{- 57}{22} + 9$

$a = - \frac{3}{22}$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$8 = \frac{- 57}{22} + 9$

$a = - \frac{3}{22}$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.2.1.1.2

Move the negative in front of the fraction.

$8 = - \frac{57}{22} + 9$

$a = - \frac{3}{22}$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$8 = - \frac{57}{22} + 9$

$a = - \frac{3}{22}$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.2.1.2

To write $9$ as a fraction with a common denominator, multiply by $\frac{22}{22}$ .

$8 = - \frac{57}{22} + 9 \cdot \frac{22}{22}$

$a = - \frac{3}{22}$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.2.1.3

Combine $9$ and $\frac{22}{22}$ .

$8 = - \frac{57}{22} + \frac{9 \cdot 22}{22}$

$a = - \frac{3}{22}$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.2.1.4

Combine the numerators over the common denominator.

$8 = \frac{- 57 + 9 \cdot 22}{22}$

$a = - \frac{3}{22}$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.2.1.5

Simplify the numerator.

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Step 1.3.4.2.1.5.1

Multiply $9$ by $22$ .

$8 = \frac{- 57 + 198}{22}$

$a = - \frac{3}{22}$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.2.1.5.2

Add $- 57$ and $198$ .

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 16 a + 9$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.3

Replace all occurrences of $a$ in $7 = 16 a + 9$ with $- \frac{3}{22}$ .

$7 = 16 (- \frac{3}{22}) + 9$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.4

Simplify the right side.

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Step 1.3.4.4.1

Simplify $16 (- \frac{3}{22}) + 9$ .

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Step 1.3.4.4.1.1

Simplify each term.

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Step 1.3.4.4.1.1.1

Cancel the common factor of $2$ .

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Step 1.3.4.4.1.1.1.1

Move the leading negative in $- \frac{3}{22}$ into the numerator.

$7 = 16 (\frac{- 3}{22}) + 9$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.4.1.1.1.2

Factor $2$ out of $16$ .

$7 = 2 (8) (\frac{- 3}{22}) + 9$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.4.1.1.1.3

Factor $2$ out of $22$ .

$7 = 2 \cdot (8 (\frac{- 3}{2 \cdot 11})) + 9$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.4.1.1.1.4

Cancel the common factor.

$7 = 2 \cdot (8 (\frac{- 3}{2 \cdot 11})) + 9$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.4.1.1.1.5

Rewrite the expression.

$7 = 8 (\frac{- 3}{11}) + 9$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$7 = 8 (\frac{- 3}{11}) + 9$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.4.1.1.2

Combine $8$ and $\frac{- 3}{11}$ .

$7 = \frac{8 \cdot - 3}{11} + 9$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.4.1.1.3

Multiply $8$ by $- 3$ .

$7 = \frac{- 24}{11} + 9$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.4.1.1.4

Move the negative in front of the fraction.

$7 = - \frac{24}{11} + 9$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$7 = - \frac{24}{11} + 9$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.4.1.2

To write $9$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$7 = - \frac{24}{11} + 9 \cdot \frac{11}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.4.1.3

Combine $9$ and $\frac{11}{11}$ .

$7 = - \frac{24}{11} + \frac{9 \cdot 11}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.4.1.4

Combine the numerators over the common denominator.

$7 = \frac{- 24 + 9 \cdot 11}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.4.1.5

Simplify the numerator.

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Step 1.3.4.4.1.5.1

Multiply $9$ by $11$ .

$7 = \frac{- 24 + 99}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.4.1.5.2

Add $- 24$ and $99$ .

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$9 = 13 a + 9$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.5

Replace all occurrences of $a$ in $9 = 13 a + 9$ with $- \frac{3}{22}$ .

$9 = 13 (- \frac{3}{22}) + 9$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.6

Simplify the right side.

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Step 1.3.4.6.1

Simplify $13 (- \frac{3}{22}) + 9$ .

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Step 1.3.4.6.1.1

Simplify each term.

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Step 1.3.4.6.1.1.1

Multiply $13 (- \frac{3}{22})$ .

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Step 1.3.4.6.1.1.1.1

Multiply $- 1$ by $13$ .

$9 = - 13 (\frac{3}{22}) + 9$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.6.1.1.1.2

Combine $- 13$ and $\frac{3}{22}$ .

$9 = \frac{- 13 \cdot 3}{22} + 9$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.6.1.1.1.3

Multiply $- 13$ by $3$ .

$9 = \frac{- 39}{22} + 9$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$9 = \frac{- 39}{22} + 9$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.6.1.1.2

Move the negative in front of the fraction.

$9 = - \frac{39}{22} + 9$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$9 = - \frac{39}{22} + 9$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.6.1.2

To write $9$ as a fraction with a common denominator, multiply by $\frac{22}{22}$ .

$9 = - \frac{39}{22} + 9 \cdot \frac{22}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.6.1.3

Combine $9$ and $\frac{22}{22}$ .

$9 = - \frac{39}{22} + \frac{9 \cdot 22}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.6.1.4

Combine the numerators over the common denominator.

$9 = \frac{- 39 + 9 \cdot 22}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.6.1.5

Simplify the numerator.

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Step 1.3.4.6.1.5.1

Multiply $9$ by $22$ .

$9 = \frac{- 39 + 198}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.6.1.5.2

Add $- 39$ and $198$ .

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$6 = 9 a + 9$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.7

Replace all occurrences of $a$ in $6 = 9 a + 9$ with $- \frac{3}{22}$ .

$6 = 9 (- \frac{3}{22}) + 9$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.8

Simplify the right side.

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Step 1.3.4.8.1

Simplify $9 (- \frac{3}{22}) + 9$ .

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Step 1.3.4.8.1.1

Simplify each term.

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Step 1.3.4.8.1.1.1

Multiply $9 (- \frac{3}{22})$ .

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Step 1.3.4.8.1.1.1.1

Multiply $- 1$ by $9$ .

$6 = - 9 (\frac{3}{22}) + 9$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.8.1.1.1.2

Combine $- 9$ and $\frac{3}{22}$ .

$6 = \frac{- 9 \cdot 3}{22} + 9$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.8.1.1.1.3

Multiply $- 9$ by $3$ .

$6 = \frac{- 27}{22} + 9$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$6 = \frac{- 27}{22} + 9$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.8.1.1.2

Move the negative in front of the fraction.

$6 = - \frac{27}{22} + 9$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$6 = - \frac{27}{22} + 9$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.8.1.2

To write $9$ as a fraction with a common denominator, multiply by $\frac{22}{22}$ .

$6 = - \frac{27}{22} + 9 \cdot \frac{22}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.8.1.3

Combine $9$ and $\frac{22}{22}$ .

$6 = - \frac{27}{22} + \frac{9 \cdot 22}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.8.1.4

Combine the numerators over the common denominator.

$6 = \frac{- 27 + 9 \cdot 22}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.8.1.5

Simplify the numerator.

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Step 1.3.4.8.1.5.1

Multiply $9$ by $22$ .

$6 = \frac{- 27 + 198}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.8.1.5.2

Add $- 27$ and $198$ .

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 6 a + 9$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.9

Replace all occurrences of $a$ in $7 = 6 a + 9$ with $- \frac{3}{22}$ .

$7 = 6 (- \frac{3}{22}) + 9$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.10

Simplify the right side.

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Step 1.3.4.10.1

Simplify $6 (- \frac{3}{22}) + 9$ .

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Step 1.3.4.10.1.1

Simplify each term.

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Step 1.3.4.10.1.1.1

Cancel the common factor of $2$ .

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Step 1.3.4.10.1.1.1.1

Move the leading negative in $- \frac{3}{22}$ into the numerator.

$7 = 6 (\frac{- 3}{22}) + 9$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.10.1.1.1.2

Factor $2$ out of $6$ .

$7 = 2 (3) (\frac{- 3}{22}) + 9$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.10.1.1.1.3

Factor $2$ out of $22$ .

$7 = 2 \cdot (3 (\frac{- 3}{2 \cdot 11})) + 9$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.10.1.1.1.4

Cancel the common factor.

$7 = 2 \cdot (3 (\frac{- 3}{2 \cdot 11})) + 9$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.10.1.1.1.5

Rewrite the expression.

$7 = 3 (\frac{- 3}{11}) + 9$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 5 a + 9$

$b = 9$

$7 = 3 (\frac{- 3}{11}) + 9$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.10.1.1.2

Combine $3$ and $\frac{- 3}{11}$ .

$7 = \frac{3 \cdot - 3}{11} + 9$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.10.1.1.3

Multiply $3$ by $- 3$ .

$7 = \frac{- 9}{11} + 9$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.10.1.1.4

Move the negative in front of the fraction.

$7 = - \frac{9}{11} + 9$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 5 a + 9$

$b = 9$

$7 = - \frac{9}{11} + 9$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.10.1.2

To write $9$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$7 = - \frac{9}{11} + 9 \cdot \frac{11}{11}$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.10.1.3

Combine $9$ and $\frac{11}{11}$ .

$7 = - \frac{9}{11} + \frac{9 \cdot 11}{11}$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.10.1.4

Combine the numerators over the common denominator.

$7 = \frac{- 9 + 9 \cdot 11}{11}$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.10.1.5

Simplify the numerator.

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Step 1.3.4.10.1.5.1

Multiply $9$ by $11$ .

$7 = \frac{- 9 + 99}{11}$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.10.1.5.2

Add $- 9$ and $99$ .

$7 = \frac{90}{11}$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 5 a + 9$

$b = 9$

$7 = \frac{90}{11}$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 5 a + 9$

$b = 9$

$7 = \frac{90}{11}$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 5 a + 9$

$b = 9$

$7 = \frac{90}{11}$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$7 = 5 a + 9$

$b = 9$

Step 1.3.4.11

Replace all occurrences of $a$ in $7 = 5 a + 9$ with $- \frac{3}{22}$ .

$7 = 5 (- \frac{3}{22}) + 9$

$7 = \frac{90}{11}$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$b = 9$

Step 1.3.4.12

Simplify the right side.

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Step 1.3.4.12.1

Simplify $5 (- \frac{3}{22}) + 9$ .

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Step 1.3.4.12.1.1

Simplify each term.

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Step 1.3.4.12.1.1.1

Multiply $5 (- \frac{3}{22})$ .

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Step 1.3.4.12.1.1.1.1

Multiply $- 1$ by $5$ .

$7 = - 5 (\frac{3}{22}) + 9$

$7 = \frac{90}{11}$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$b = 9$

Step 1.3.4.12.1.1.1.2

Combine $- 5$ and $\frac{3}{22}$ .

$7 = \frac{- 5 \cdot 3}{22} + 9$

$7 = \frac{90}{11}$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$b = 9$

Step 1.3.4.12.1.1.1.3

Multiply $- 5$ by $3$ .

$7 = \frac{- 15}{22} + 9$

$7 = \frac{90}{11}$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$b = 9$

$7 = \frac{- 15}{22} + 9$

$7 = \frac{90}{11}$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$b = 9$

Step 1.3.4.12.1.1.2

Move the negative in front of the fraction.

$7 = - \frac{15}{22} + 9$

$7 = \frac{90}{11}$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$b = 9$

$7 = - \frac{15}{22} + 9$

$7 = \frac{90}{11}$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$b = 9$

Step 1.3.4.12.1.2

To write $9$ as a fraction with a common denominator, multiply by $\frac{22}{22}$ .

$7 = - \frac{15}{22} + 9 \cdot \frac{22}{22}$

$7 = \frac{90}{11}$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$b = 9$

Step 1.3.4.12.1.3

Combine $9$ and $\frac{22}{22}$ .

$7 = - \frac{15}{22} + \frac{9 \cdot 22}{22}$

$7 = \frac{90}{11}$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$b = 9$

Step 1.3.4.12.1.4

Combine the numerators over the common denominator.

$7 = \frac{- 15 + 9 \cdot 22}{22}$

$7 = \frac{90}{11}$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$b = 9$

Step 1.3.4.12.1.5

Simplify the numerator.

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Step 1.3.4.12.1.5.1

Multiply $9$ by $22$ .

$7 = \frac{- 15 + 198}{22}$

$7 = \frac{90}{11}$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$b = 9$

Step 1.3.4.12.1.5.2

Add $- 15$ and $198$ .

$7 = \frac{183}{22}$

$7 = \frac{90}{11}$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$b = 9$

$7 = \frac{183}{22}$

$7 = \frac{90}{11}$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$b = 9$

$7 = \frac{183}{22}$

$7 = \frac{90}{11}$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$b = 9$

$7 = \frac{183}{22}$

$7 = \frac{90}{11}$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$b = 9$

$7 = \frac{183}{22}$

$7 = \frac{90}{11}$

$6 = \frac{171}{22}$

$9 = \frac{159}{22}$

$7 = \frac{75}{11}$

$8 = \frac{141}{22}$

$a = - \frac{3}{22}$

$b = 9$

Step 1.3.5

Since $7 = \frac{183}{22}$ is not true, there is no solution.

No solution

Step 1.4

Since $y \neq y$ for the corresponding $x$ values, the function is not linear.

The function is not linear

Step 2

Check if the function rule is quadratic.

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Step 2.1

To find if the table follows a function rule, check whether the function rule could follow the form $y = a x^{2} + b x + c$ .

$y = a x^{2} + b x + c$

Step 2.2

Build a set of $3$ equations from the table such that $y = a x^{2} + b x + c$ .

Step 2.3

Calculate the values of $a$ , $b$ , and $c$ .

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Step 2.3.1

Solve for $c$ in $9 = a \cdot 0^{2} + c$ .

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Step 2.3.1.1

Rewrite the equation as $a \cdot 0^{2} + c = 9$ .

$a \cdot 0^{2} + c = 9$

$7 = a \cdot 5^{2} + b (5) + c$

$7 = a \cdot 6^{2} + b (6) + c$

$6 = a \cdot 9^{2} + b (9) + c$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.1.2

Simplify $a \cdot 0^{2} + c$ .

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Step 2.3.1.2.1

Simplify each term.

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Step 2.3.1.2.1.1

Raising $0$ to any positive power yields $0$ .

$a \cdot 0 + c = 9$

$7 = a \cdot 5^{2} + b (5) + c$

$7 = a \cdot 6^{2} + b (6) + c$

$6 = a \cdot 9^{2} + b (9) + c$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.1.2.1.2

Multiply $a$ by $0$ .

$0 + c = 9$

$7 = a \cdot 5^{2} + b (5) + c$

$7 = a \cdot 6^{2} + b (6) + c$

$6 = a \cdot 9^{2} + b (9) + c$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

$0 + c = 9$

$7 = a \cdot 5^{2} + b (5) + c$

$7 = a \cdot 6^{2} + b (6) + c$

$6 = a \cdot 9^{2} + b (9) + c$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.1.2.2

Add $0$ and $c$ .

$c = 9$

$7 = a \cdot 5^{2} + b (5) + c$

$7 = a \cdot 6^{2} + b (6) + c$

$6 = a \cdot 9^{2} + b (9) + c$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

$c = 9$

$7 = a \cdot 5^{2} + b (5) + c$

$7 = a \cdot 6^{2} + b (6) + c$

$6 = a \cdot 9^{2} + b (9) + c$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

$c = 9$

$7 = a \cdot 5^{2} + b (5) + c$

$7 = a \cdot 6^{2} + b (6) + c$

$6 = a \cdot 9^{2} + b (9) + c$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2

Replace all occurrences of $c$ with $9$ in each equation.

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Step 2.3.2.1

Replace all occurrences of $c$ in $7 = a \cdot 5^{2} + b (5) + c$ with $9$ .

$7 = a \cdot 5^{2} + b (5) + 9$

$c = 9$

$7 = a \cdot 6^{2} + b (6) + c$

$6 = a \cdot 9^{2} + b (9) + c$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.2

Simplify $7 = a \cdot 5^{2} + b (5) + 9$ .

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Step 2.3.2.2.1

Simplify the left side.

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Step 2.3.2.2.1.1

Remove parentheses.

$7 = a \cdot 5^{2} + b (5) + 9$

$c = 9$

$7 = a \cdot 6^{2} + b (6) + c$

$6 = a \cdot 9^{2} + b (9) + c$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

$7 = a \cdot 5^{2} + b (5) + 9$

$c = 9$

$7 = a \cdot 6^{2} + b (6) + c$

$6 = a \cdot 9^{2} + b (9) + c$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.2.2

Simplify the right side.

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Step 2.3.2.2.2.1

Simplify each term.

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Step 2.3.2.2.2.1.1

Raise $5$ to the power of $2$ .

$7 = a \cdot 25 + b (5) + 9$

$c = 9$

$7 = a \cdot 6^{2} + b (6) + c$

$6 = a \cdot 9^{2} + b (9) + c$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.2.2.1.2

Move $25$ to the left of $a$ .

$7 = 25 \cdot a + b (5) + 9$

$c = 9$

$7 = a \cdot 6^{2} + b (6) + c$

$6 = a \cdot 9^{2} + b (9) + c$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.2.2.1.3

Move $5$ to the left of $b$ .

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = a \cdot 6^{2} + b (6) + c$

$6 = a \cdot 9^{2} + b (9) + c$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = a \cdot 6^{2} + b (6) + c$

$6 = a \cdot 9^{2} + b (9) + c$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = a \cdot 6^{2} + b (6) + c$

$6 = a \cdot 9^{2} + b (9) + c$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = a \cdot 6^{2} + b (6) + c$

$6 = a \cdot 9^{2} + b (9) + c$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.3

Replace all occurrences of $c$ in $7 = a \cdot 6^{2} + b (6) + c$ with $9$ .

$7 = a \cdot 6^{2} + b (6) + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = a \cdot 9^{2} + b (9) + c$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.4

Simplify $7 = a \cdot 6^{2} + b (6) + 9$ .

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Step 2.3.2.4.1

Simplify the left side.

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Step 2.3.2.4.1.1

Remove parentheses.

$7 = a \cdot 6^{2} + b (6) + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = a \cdot 9^{2} + b (9) + c$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

$7 = a \cdot 6^{2} + b (6) + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = a \cdot 9^{2} + b (9) + c$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.4.2

Simplify the right side.

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Step 2.3.2.4.2.1

Simplify each term.

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Step 2.3.2.4.2.1.1

Raise $6$ to the power of $2$ .

$7 = a \cdot 36 + b (6) + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = a \cdot 9^{2} + b (9) + c$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.4.2.1.2

Move $36$ to the left of $a$ .

$7 = 36 \cdot a + b (6) + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = a \cdot 9^{2} + b (9) + c$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.4.2.1.3

Move $6$ to the left of $b$ .

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = a \cdot 9^{2} + b (9) + c$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = a \cdot 9^{2} + b (9) + c$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = a \cdot 9^{2} + b (9) + c$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = a \cdot 9^{2} + b (9) + c$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.5

Replace all occurrences of $c$ in $6 = a \cdot 9^{2} + b (9) + c$ with $9$ .

$6 = a \cdot 9^{2} + b (9) + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.6

Simplify $6 = a \cdot 9^{2} + b (9) + 9$ .

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Step 2.3.2.6.1

Simplify the left side.

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Step 2.3.2.6.1.1

Remove parentheses.

$6 = a \cdot 9^{2} + b (9) + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

$6 = a \cdot 9^{2} + b (9) + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.6.2

Simplify the right side.

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Step 2.3.2.6.2.1

Simplify each term.

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Step 2.3.2.6.2.1.1

Raise $9$ to the power of $2$ .

$6 = a \cdot 81 + b (9) + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.6.2.1.2

Move $81$ to the left of $a$ .

$6 = 81 \cdot a + b (9) + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.6.2.1.3

Move $9$ to the left of $b$ .

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$9 = a \cdot 13^{2} + b (13) + c$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.7

Replace all occurrences of $c$ in $9 = a \cdot 13^{2} + b (13) + c$ with $9$ .

$9 = a \cdot 13^{2} + b (13) + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.8

Simplify $9 = a \cdot 13^{2} + b (13) + 9$ .

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Step 2.3.2.8.1

Simplify the left side.

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Step 2.3.2.8.1.1

Remove parentheses.

$9 = a \cdot 13^{2} + b (13) + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

$9 = a \cdot 13^{2} + b (13) + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.8.2

Simplify the right side.

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Step 2.3.2.8.2.1

Simplify each term.

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Step 2.3.2.8.2.1.1

Raise $13$ to the power of $2$ .

$9 = a \cdot 169 + b (13) + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.8.2.1.2

Move $169$ to the left of $a$ .

$9 = 169 \cdot a + b (13) + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.8.2.1.3

Move $13$ to the left of $b$ .

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = a \cdot 16^{2} + b (16) + c$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.9

Replace all occurrences of $c$ in $7 = a \cdot 16^{2} + b (16) + c$ with $9$ .

$7 = a \cdot 16^{2} + b (16) + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.10

Simplify $7 = a \cdot 16^{2} + b (16) + 9$ .

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Step 2.3.2.10.1

Simplify the left side.

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Step 2.3.2.10.1.1

Remove parentheses.

$7 = a \cdot 16^{2} + b (16) + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

$7 = a \cdot 16^{2} + b (16) + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.10.2

Simplify the right side.

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Step 2.3.2.10.2.1

Simplify each term.

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Step 2.3.2.10.2.1.1

Raise $16$ to the power of $2$ .

$7 = a \cdot 256 + b (16) + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.10.2.1.2

Move $256$ to the left of $a$ .

$7 = 256 \cdot a + b (16) + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.10.2.1.3

Move $16$ to the left of $b$ .

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$8 = a \cdot 19^{2} + b (19) + c$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.11

Replace all occurrences of $c$ in $8 = a \cdot 19^{2} + b (19) + c$ with $9$ .

$8 = a \cdot 19^{2} + b (19) + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.12

Simplify $8 = a \cdot 19^{2} + b (19) + 9$ .

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Step 2.3.2.12.1

Simplify the left side.

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Step 2.3.2.12.1.1

Remove parentheses.

$8 = a \cdot 19^{2} + b (19) + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = a \cdot 22^{2} + b (22) + c$

$8 = a \cdot 19^{2} + b (19) + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.12.2

Simplify the right side.

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Step 2.3.2.12.2.1

Simplify each term.

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Step 2.3.2.12.2.1.1

Raise $19$ to the power of $2$ .

$8 = a \cdot 361 + b (19) + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.12.2.1.2

Move $361$ to the left of $a$ .

$8 = 361 \cdot a + b (19) + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.12.2.1.3

Move $19$ to the left of $b$ .

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = a \cdot 22^{2} + b (22) + c$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = a \cdot 22^{2} + b (22) + c$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = a \cdot 22^{2} + b (22) + c$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = a \cdot 22^{2} + b (22) + c$

Step 2.3.2.13

Replace all occurrences of $c$ in $6 = a \cdot 22^{2} + b (22) + c$ with $9$ .

$6 = a \cdot 22^{2} + b (22) + 9$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.2.14

Simplify $6 = a \cdot 22^{2} + b (22) + 9$ .

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Step 2.3.2.14.1

Simplify the left side.

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Step 2.3.2.14.1.1

Remove parentheses.

$6 = a \cdot 22^{2} + b (22) + 9$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = a \cdot 22^{2} + b (22) + 9$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.2.14.2

Simplify the right side.

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Step 2.3.2.14.2.1

Simplify each term.

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Step 2.3.2.14.2.1.1

Raise $22$ to the power of $2$ .

$6 = a \cdot 484 + b (22) + 9$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.2.14.2.1.2

Move $484$ to the left of $a$ .

$6 = 484 \cdot a + b (22) + 9$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.2.14.2.1.3

Move $22$ to the left of $b$ .

$6 = 484 a + 22 b + 9$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = 484 a + 22 b + 9$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = 484 a + 22 b + 9$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = 484 a + 22 b + 9$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = 484 a + 22 b + 9$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.3

Solve for $a$ in $6 = 484 a + 22 b + 9$ .

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Step 2.3.3.1

Rewrite the equation as $484 a + 22 b + 9 = 6$ .

$484 a + 22 b + 9 = 6$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.3.2

Move all terms not containing $a$ to the right side of the equation.

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Step 2.3.3.2.1

Subtract $22 b$ from both sides of the equation.

$484 a + 9 = 6 - 22 b$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.3.2.2

Subtract $9$ from both sides of the equation.

$484 a = 6 - 22 b - 9$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.3.2.3

Subtract $9$ from $6$ .

$484 a = - 22 b - 3$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$484 a = - 22 b - 3$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.3.3

Divide each term in $484 a = - 22 b - 3$ by $484$ and simplify.

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Step 2.3.3.3.1

Divide each term in $484 a = - 22 b - 3$ by $484$ .

$\frac{484 a}{484} = \frac{- 22 b}{484} + \frac{- 3}{484}$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.3.3.2

Simplify the left side.

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Step 2.3.3.3.2.1

Cancel the common factor of $484$ .

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Step 2.3.3.3.2.1.1

Cancel the common factor.

$\frac{484 a}{484} = \frac{- 22 b}{484} + \frac{- 3}{484}$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.3.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 22 b}{484} + \frac{- 3}{484}$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$a = \frac{- 22 b}{484} + \frac{- 3}{484}$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$a = \frac{- 22 b}{484} + \frac{- 3}{484}$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.3.3.3

Simplify the right side.

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Step 2.3.3.3.3.1

Simplify each term.

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Step 2.3.3.3.3.1.1

Cancel the common factor of $- 22$ and $484$ .

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Step 2.3.3.3.3.1.1.1

Factor $22$ out of $- 22 b$ .

$a = \frac{22 (- b)}{484} + \frac{- 3}{484}$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.3.3.3.1.1.2

Cancel the common factors.

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Step 2.3.3.3.3.1.1.2.1

Factor $22$ out of $484$ .

$a = \frac{22 (- b)}{22 (22)} + \frac{- 3}{484}$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.3.3.3.1.1.2.2

Cancel the common factor.

$a = \frac{22 (- b)}{22 \cdot 22} + \frac{- 3}{484}$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.3.3.3.1.1.2.3

Rewrite the expression.

$a = \frac{- b}{22} + \frac{- 3}{484}$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$a = \frac{- b}{22} + \frac{- 3}{484}$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$a = \frac{- b}{22} + \frac{- 3}{484}$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.3.3.3.1.2

Move the negative in front of the fraction.

$a = - \frac{b}{22} + \frac{- 3}{484}$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.3.3.3.1.3

Move the negative in front of the fraction.

$a = - \frac{b}{22} - \frac{3}{484}$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$a = - \frac{b}{22} - \frac{3}{484}$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$a = - \frac{b}{22} - \frac{3}{484}$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$a = - \frac{b}{22} - \frac{3}{484}$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$a = - \frac{b}{22} - \frac{3}{484}$

$8 = 361 a + 19 b + 9$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4

Replace all occurrences of $a$ with $- \frac{b}{22} - \frac{3}{484}$ in each equation.

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Step 2.3.4.1

Replace all occurrences of $a$ in $8 = 361 a + 19 b + 9$ with $- \frac{b}{22} - \frac{3}{484}$ .

$8 = 361 (- \frac{b}{22} - \frac{3}{484}) + 19 b + 9$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.2

Simplify the right side.

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Step 2.3.4.2.1

Simplify $361 (- \frac{b}{22} - \frac{3}{484}) + 19 b + 9$ .

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Step 2.3.4.2.1.1

Simplify each term.

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Step 2.3.4.2.1.1.1

Apply the distributive property.

$8 = 361 (- \frac{b}{22}) + 361 (- \frac{3}{484}) + 19 b + 9$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.2.1.1.2

Multiply $361 (- \frac{b}{22})$ .

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Step 2.3.4.2.1.1.2.1

Multiply $- 1$ by $361$ .

$8 = - 361 \frac{b}{22} + 361 (- \frac{3}{484}) + 19 b + 9$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.2.1.1.2.2

Combine $- 361$ and $\frac{b}{22}$ .

$8 = \frac{- 361 b}{22} + 361 (- \frac{3}{484}) + 19 b + 9$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$8 = \frac{- 361 b}{22} + 361 (- \frac{3}{484}) + 19 b + 9$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.2.1.1.3

Multiply $361 (- \frac{3}{484})$ .

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Step 2.3.4.2.1.1.3.1

Multiply $- 1$ by $361$ .

$8 = \frac{- 361 b}{22} - 361 (\frac{3}{484}) + 19 b + 9$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.2.1.1.3.2

Combine $- 361$ and $\frac{3}{484}$ .

$8 = \frac{- 361 b}{22} + \frac{- 361 \cdot 3}{484} + 19 b + 9$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.2.1.1.3.3

Multiply $- 361$ by $3$ .

$8 = \frac{- 361 b}{22} + \frac{- 1083}{484} + 19 b + 9$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$8 = \frac{- 361 b}{22} + \frac{- 1083}{484} + 19 b + 9$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.2.1.1.4

Simplify each term.

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Step 2.3.4.2.1.1.4.1

Move the negative in front of the fraction.

$8 = - \frac{361 b}{22} + \frac{- 1083}{484} + 19 b + 9$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.2.1.1.4.2

Move the negative in front of the fraction.

$8 = - \frac{361 b}{22} - \frac{1083}{484} + 19 b + 9$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$8 = - \frac{361 b}{22} - \frac{1083}{484} + 19 b + 9$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$8 = - \frac{361 b}{22} - \frac{1083}{484} + 19 b + 9$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.2.1.2

To write $19 b$ as a fraction with a common denominator, multiply by $\frac{22}{22}$ .

$8 = - \frac{361 b}{22} + 19 b \cdot \frac{22}{22} - \frac{1083}{484} + 9$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.2.1.3

Combine $19 b$ and $\frac{22}{22}$ .

$8 = - \frac{361 b}{22} + \frac{19 b \cdot 22}{22} - \frac{1083}{484} + 9$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.2.1.4

Combine the numerators over the common denominator.

$8 = \frac{- 361 b + 19 b \cdot 22}{22} - \frac{1083}{484} + 9$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.2.1.5

Find the common denominator.

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Step 2.3.4.2.1.5.1

Multiply $\frac{- 361 b + 19 b \cdot 22}{22}$ by $\frac{22}{22}$ .

$8 = \frac{- 361 b + 19 b \cdot 22}{22} \cdot \frac{22}{22} - \frac{1083}{484} + 9$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.2.1.5.2

Multiply $\frac{- 361 b + 19 b \cdot 22}{22}$ by $\frac{22}{22}$ .

$8 = \frac{(- 361 b + 19 b \cdot 22) \cdot 22}{22 \cdot 22} - \frac{1083}{484} + 9$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.2.1.5.3

Write $9$ as a fraction with denominator $1$ .

$8 = \frac{(- 361 b + 19 b \cdot 22) \cdot 22}{22 \cdot 22} - \frac{1083}{484} + \frac{9}{1}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.2.1.5.4

Multiply $\frac{9}{1}$ by $\frac{484}{484}$ .

$8 = \frac{(- 361 b + 19 b \cdot 22) \cdot 22}{22 \cdot 22} - \frac{1083}{484} + \frac{9}{1} \cdot \frac{484}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.2.1.5.5

Multiply $\frac{9}{1}$ by $\frac{484}{484}$ .

$8 = \frac{(- 361 b + 19 b \cdot 22) \cdot 22}{22 \cdot 22} - \frac{1083}{484} + \frac{9 \cdot 484}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.2.1.5.6

Multiply $22$ by $22$ .

$8 = \frac{(- 361 b + 19 b \cdot 22) \cdot 22}{484} - \frac{1083}{484} + \frac{9 \cdot 484}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$8 = \frac{(- 361 b + 19 b \cdot 22) \cdot 22}{484} - \frac{1083}{484} + \frac{9 \cdot 484}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.2.1.6

Combine the numerators over the common denominator.

$8 = \frac{(- 361 b + 19 b \cdot 22) \cdot 22 - 1083 + 9 \cdot 484}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.2.1.7

Simplify each term.

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Step 2.3.4.2.1.7.1

Multiply $22$ by $19$ .

$8 = \frac{(- 361 b + 418 b) \cdot 22 - 1083 + 9 \cdot 484}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.2.1.7.2

Add $- 361 b$ and $418 b$ .

$8 = \frac{57 b \cdot 22 - 1083 + 9 \cdot 484}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.2.1.7.3

Multiply $22$ by $57$ .

$8 = \frac{1254 b - 1083 + 9 \cdot 484}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.2.1.7.4

Multiply $9$ by $484$ .

$8 = \frac{1254 b - 1083 + 4356}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$8 = \frac{1254 b - 1083 + 4356}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.2.1.8

Simplify with factoring out.

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Step 2.3.4.2.1.8.1

Add $- 1083$ and $4356$ .

$8 = \frac{1254 b + 3273}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.2.1.8.2

Factor $3$ out of $1254 b + 3273$ .

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Step 2.3.4.2.1.8.2.1

Factor $3$ out of $1254 b$ .

$8 = \frac{3 (418 b) + 3273}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.2.1.8.2.2

Factor $3$ out of $3273$ .

$8 = \frac{3 (418 b) + 3 (1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.2.1.8.2.3

Factor $3$ out of $3 (418 b) + 3 (1091)$ .

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 256 a + 16 b + 9$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.3

Replace all occurrences of $a$ in $7 = 256 a + 16 b + 9$ with $- \frac{b}{22} - \frac{3}{484}$ .

$7 = 256 (- \frac{b}{22} - \frac{3}{484}) + 16 b + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4

Simplify the right side.

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Step 2.3.4.4.1

Simplify $256 (- \frac{b}{22} - \frac{3}{484}) + 16 b + 9$ .

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Step 2.3.4.4.1.1

Simplify each term.

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Step 2.3.4.4.1.1.1

Apply the distributive property.

$7 = 256 (- \frac{b}{22}) + 256 (- \frac{3}{484}) + 16 b + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.1.2

Cancel the common factor of $2$ .

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Step 2.3.4.4.1.1.2.1

Move the leading negative in $- \frac{b}{22}$ into the numerator.

$7 = 256 (\frac{- b}{22}) + 256 (- \frac{3}{484}) + 16 b + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.1.2.2

Factor $2$ out of $256$ .

$7 = 2 (128) (\frac{- b}{22}) + 256 (- \frac{3}{484}) + 16 b + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.1.2.3

Factor $2$ out of $22$ .

$7 = 2 \cdot (128 (\frac{- b}{2 \cdot 11})) + 256 (- \frac{3}{484}) + 16 b + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.1.2.4

Cancel the common factor.

$7 = 2 \cdot (128 (\frac{- b}{2 \cdot 11})) + 256 (- \frac{3}{484}) + 16 b + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.1.2.5

Rewrite the expression.

$7 = 128 (\frac{- b}{11}) + 256 (- \frac{3}{484}) + 16 b + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = 128 (\frac{- b}{11}) + 256 (- \frac{3}{484}) + 16 b + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.1.3

Combine $128$ and $\frac{- b}{11}$ .

$7 = \frac{128 (- b)}{11} + 256 (- \frac{3}{484}) + 16 b + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.1.4

Multiply $- 1$ by $128$ .

$7 = \frac{- 128 b}{11} + 256 (- \frac{3}{484}) + 16 b + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.1.5

Cancel the common factor of $4$ .

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Step 2.3.4.4.1.1.5.1

Move the leading negative in $- \frac{3}{484}$ into the numerator.

$7 = \frac{- 128 b}{11} + 256 (\frac{- 3}{484}) + 16 b + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.1.5.2

Factor $4$ out of $256$ .

$7 = \frac{- 128 b}{11} + 4 (64) (\frac{- 3}{484}) + 16 b + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.1.5.3

Factor $4$ out of $484$ .

$7 = \frac{- 128 b}{11} + 4 \cdot (64 (\frac{- 3}{4 \cdot 121})) + 16 b + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.1.5.4

Cancel the common factor.

$7 = \frac{- 128 b}{11} + 4 \cdot (64 (\frac{- 3}{4 \cdot 121})) + 16 b + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.1.5.5

Rewrite the expression.

$7 = \frac{- 128 b}{11} + 64 (\frac{- 3}{121}) + 16 b + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = \frac{- 128 b}{11} + 64 (\frac{- 3}{121}) + 16 b + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.1.6

Combine $64$ and $\frac{- 3}{121}$ .

$7 = \frac{- 128 b}{11} + \frac{64 \cdot - 3}{121} + 16 b + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.1.7

Multiply $64$ by $- 3$ .

$7 = \frac{- 128 b}{11} + \frac{- 192}{121} + 16 b + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.1.8

Simplify each term.

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Step 2.3.4.4.1.1.8.1

Move the negative in front of the fraction.

$7 = - \frac{128 b}{11} + \frac{- 192}{121} + 16 b + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.1.8.2

Move the negative in front of the fraction.

$7 = - \frac{128 b}{11} - \frac{192}{121} + 16 b + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = - \frac{128 b}{11} - \frac{192}{121} + 16 b + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = - \frac{128 b}{11} - \frac{192}{121} + 16 b + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.2

To write $16 b$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$7 = - \frac{128 b}{11} + 16 b \cdot \frac{11}{11} - \frac{192}{121} + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.3

Combine $16 b$ and $\frac{11}{11}$ .

$7 = - \frac{128 b}{11} + \frac{16 b \cdot 11}{11} - \frac{192}{121} + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.4

Combine the numerators over the common denominator.

$7 = \frac{- 128 b + 16 b \cdot 11}{11} - \frac{192}{121} + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.5

Find the common denominator.

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Step 2.3.4.4.1.5.1

Multiply $\frac{- 128 b + 16 b \cdot 11}{11}$ by $\frac{11}{11}$ .

$7 = \frac{- 128 b + 16 b \cdot 11}{11} \cdot \frac{11}{11} - \frac{192}{121} + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.5.2

Multiply $\frac{- 128 b + 16 b \cdot 11}{11}$ by $\frac{11}{11}$ .

$7 = \frac{(- 128 b + 16 b \cdot 11) \cdot 11}{11 \cdot 11} - \frac{192}{121} + 9$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.5.3

Write $9$ as a fraction with denominator $1$ .

$7 = \frac{(- 128 b + 16 b \cdot 11) \cdot 11}{11 \cdot 11} - \frac{192}{121} + \frac{9}{1}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.5.4

Multiply $\frac{9}{1}$ by $\frac{121}{121}$ .

$7 = \frac{(- 128 b + 16 b \cdot 11) \cdot 11}{11 \cdot 11} - \frac{192}{121} + \frac{9}{1} \cdot \frac{121}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.5.5

Multiply $\frac{9}{1}$ by $\frac{121}{121}$ .

$7 = \frac{(- 128 b + 16 b \cdot 11) \cdot 11}{11 \cdot 11} - \frac{192}{121} + \frac{9 \cdot 121}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.5.6

Multiply $11$ by $11$ .

$7 = \frac{(- 128 b + 16 b \cdot 11) \cdot 11}{121} - \frac{192}{121} + \frac{9 \cdot 121}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = \frac{(- 128 b + 16 b \cdot 11) \cdot 11}{121} - \frac{192}{121} + \frac{9 \cdot 121}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.6

Combine the numerators over the common denominator.

$7 = \frac{(- 128 b + 16 b \cdot 11) \cdot 11 - 192 + 9 \cdot 121}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.7

Simplify each term.

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Step 2.3.4.4.1.7.1

Multiply $11$ by $16$ .

$7 = \frac{(- 128 b + 176 b) \cdot 11 - 192 + 9 \cdot 121}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.7.2

Add $- 128 b$ and $176 b$ .

$7 = \frac{48 b \cdot 11 - 192 + 9 \cdot 121}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.7.3

Multiply $11$ by $48$ .

$7 = \frac{528 b - 192 + 9 \cdot 121}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.7.4

Multiply $9$ by $121$ .

$7 = \frac{528 b - 192 + 1089}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = \frac{528 b - 192 + 1089}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.8

Simplify with factoring out.

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Step 2.3.4.4.1.8.1

Add $- 192$ and $1089$ .

$7 = \frac{528 b + 897}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.8.2

Factor $3$ out of $528 b + 897$ .

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Step 2.3.4.4.1.8.2.1

Factor $3$ out of $528 b$ .

$7 = \frac{3 (176 b) + 897}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.8.2.2

Factor $3$ out of $897$ .

$7 = \frac{3 (176 b) + 3 (299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.4.1.8.2.3

Factor $3$ out of $3 (176 b) + 3 (299)$ .

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$9 = 169 a + 13 b + 9$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.5

Replace all occurrences of $a$ in $9 = 169 a + 13 b + 9$ with $- \frac{b}{22} - \frac{3}{484}$ .

$9 = 169 (- \frac{b}{22} - \frac{3}{484}) + 13 b + 9$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.6

Simplify the right side.

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Step 2.3.4.6.1

Simplify $169 (- \frac{b}{22} - \frac{3}{484}) + 13 b + 9$ .

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Step 2.3.4.6.1.1

Simplify each term.

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Step 2.3.4.6.1.1.1

Apply the distributive property.

$9 = 169 (- \frac{b}{22}) + 169 (- \frac{3}{484}) + 13 b + 9$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.6.1.1.2

Multiply $169 (- \frac{b}{22})$ .

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Step 2.3.4.6.1.1.2.1

Multiply $- 1$ by $169$ .

$9 = - 169 \frac{b}{22} + 169 (- \frac{3}{484}) + 13 b + 9$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.6.1.1.2.2

Combine $- 169$ and $\frac{b}{22}$ .

$9 = \frac{- 169 b}{22} + 169 (- \frac{3}{484}) + 13 b + 9$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$9 = \frac{- 169 b}{22} + 169 (- \frac{3}{484}) + 13 b + 9$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.6.1.1.3

Multiply $169 (- \frac{3}{484})$ .

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Step 2.3.4.6.1.1.3.1

Multiply $- 1$ by $169$ .

$9 = \frac{- 169 b}{22} - 169 (\frac{3}{484}) + 13 b + 9$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.6.1.1.3.2

Combine $- 169$ and $\frac{3}{484}$ .

$9 = \frac{- 169 b}{22} + \frac{- 169 \cdot 3}{484} + 13 b + 9$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.6.1.1.3.3

Multiply $- 169$ by $3$ .

$9 = \frac{- 169 b}{22} + \frac{- 507}{484} + 13 b + 9$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$9 = \frac{- 169 b}{22} + \frac{- 507}{484} + 13 b + 9$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.6.1.1.4

Simplify each term.

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Step 2.3.4.6.1.1.4.1

Move the negative in front of the fraction.

$9 = - \frac{169 b}{22} + \frac{- 507}{484} + 13 b + 9$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.6.1.1.4.2

Move the negative in front of the fraction.

$9 = - \frac{169 b}{22} - \frac{507}{484} + 13 b + 9$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$9 = - \frac{169 b}{22} - \frac{507}{484} + 13 b + 9$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$9 = - \frac{169 b}{22} - \frac{507}{484} + 13 b + 9$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.6.1.2

To write $13 b$ as a fraction with a common denominator, multiply by $\frac{22}{22}$ .

$9 = - \frac{169 b}{22} + 13 b \cdot \frac{22}{22} - \frac{507}{484} + 9$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.6.1.3

Combine $13 b$ and $\frac{22}{22}$ .

$9 = - \frac{169 b}{22} + \frac{13 b \cdot 22}{22} - \frac{507}{484} + 9$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.6.1.4

Combine the numerators over the common denominator.

$9 = \frac{- 169 b + 13 b \cdot 22}{22} - \frac{507}{484} + 9$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.6.1.5

Find the common denominator.

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Step 2.3.4.6.1.5.1

Multiply $\frac{- 169 b + 13 b \cdot 22}{22}$ by $\frac{22}{22}$ .

$9 = \frac{- 169 b + 13 b \cdot 22}{22} \cdot \frac{22}{22} - \frac{507}{484} + 9$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.6.1.5.2

Multiply $\frac{- 169 b + 13 b \cdot 22}{22}$ by $\frac{22}{22}$ .

$9 = \frac{(- 169 b + 13 b \cdot 22) \cdot 22}{22 \cdot 22} - \frac{507}{484} + 9$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.6.1.5.3

Write $9$ as a fraction with denominator $1$ .

$9 = \frac{(- 169 b + 13 b \cdot 22) \cdot 22}{22 \cdot 22} - \frac{507}{484} + \frac{9}{1}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.6.1.5.4

Multiply $\frac{9}{1}$ by $\frac{484}{484}$ .

$9 = \frac{(- 169 b + 13 b \cdot 22) \cdot 22}{22 \cdot 22} - \frac{507}{484} + \frac{9}{1} \cdot \frac{484}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.6.1.5.5

Multiply $\frac{9}{1}$ by $\frac{484}{484}$ .

$9 = \frac{(- 169 b + 13 b \cdot 22) \cdot 22}{22 \cdot 22} - \frac{507}{484} + \frac{9 \cdot 484}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.6.1.5.6

Multiply $22$ by $22$ .

$9 = \frac{(- 169 b + 13 b \cdot 22) \cdot 22}{484} - \frac{507}{484} + \frac{9 \cdot 484}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$9 = \frac{(- 169 b + 13 b \cdot 22) \cdot 22}{484} - \frac{507}{484} + \frac{9 \cdot 484}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.6.1.6

Combine the numerators over the common denominator.

$9 = \frac{(- 169 b + 13 b \cdot 22) \cdot 22 - 507 + 9 \cdot 484}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.6.1.7

Simplify each term.

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Step 2.3.4.6.1.7.1

Multiply $22$ by $13$ .

$9 = \frac{(- 169 b + 286 b) \cdot 22 - 507 + 9 \cdot 484}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.6.1.7.2

Add $- 169 b$ and $286 b$ .

$9 = \frac{117 b \cdot 22 - 507 + 9 \cdot 484}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.6.1.7.3

Multiply $22$ by $117$ .

$9 = \frac{2574 b - 507 + 9 \cdot 484}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.6.1.7.4

Multiply $9$ by $484$ .

$9 = \frac{2574 b - 507 + 4356}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$9 = \frac{2574 b - 507 + 4356}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.6.1.8

Simplify with factoring out.

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Step 2.3.4.6.1.8.1

Add $- 507$ and $4356$ .

$9 = \frac{2574 b + 3849}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.6.1.8.2

Factor $3$ out of $2574 b + 3849$ .

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Step 2.3.4.6.1.8.2.1

Factor $3$ out of $2574 b$ .

$9 = \frac{3 (858 b) + 3849}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.6.1.8.2.2

Factor $3$ out of $3849$ .

$9 = \frac{3 (858 b) + 3 (1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.6.1.8.2.3

Factor $3$ out of $3 (858 b) + 3 (1283)$ .

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$6 = 81 a + 9 b + 9$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.7

Replace all occurrences of $a$ in $6 = 81 a + 9 b + 9$ with $- \frac{b}{22} - \frac{3}{484}$ .

$6 = 81 (- \frac{b}{22} - \frac{3}{484}) + 9 b + 9$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.8

Simplify the right side.

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Step 2.3.4.8.1

Simplify $81 (- \frac{b}{22} - \frac{3}{484}) + 9 b + 9$ .

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Step 2.3.4.8.1.1

Simplify each term.

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Step 2.3.4.8.1.1.1

Apply the distributive property.

$6 = 81 (- \frac{b}{22}) + 81 (- \frac{3}{484}) + 9 b + 9$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.8.1.1.2

Multiply $81 (- \frac{b}{22})$ .

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Step 2.3.4.8.1.1.2.1

Multiply $- 1$ by $81$ .

$6 = - 81 \frac{b}{22} + 81 (- \frac{3}{484}) + 9 b + 9$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.8.1.1.2.2

Combine $- 81$ and $\frac{b}{22}$ .

$6 = \frac{- 81 b}{22} + 81 (- \frac{3}{484}) + 9 b + 9$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = \frac{- 81 b}{22} + 81 (- \frac{3}{484}) + 9 b + 9$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.8.1.1.3

Multiply $81 (- \frac{3}{484})$ .

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Step 2.3.4.8.1.1.3.1

Multiply $- 1$ by $81$ .

$6 = \frac{- 81 b}{22} - 81 (\frac{3}{484}) + 9 b + 9$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.8.1.1.3.2

Combine $- 81$ and $\frac{3}{484}$ .

$6 = \frac{- 81 b}{22} + \frac{- 81 \cdot 3}{484} + 9 b + 9$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.8.1.1.3.3

Multiply $- 81$ by $3$ .

$6 = \frac{- 81 b}{22} + \frac{- 243}{484} + 9 b + 9$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = \frac{- 81 b}{22} + \frac{- 243}{484} + 9 b + 9$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.8.1.1.4

Simplify each term.

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Step 2.3.4.8.1.1.4.1

Move the negative in front of the fraction.

$6 = - \frac{81 b}{22} + \frac{- 243}{484} + 9 b + 9$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.8.1.1.4.2

Move the negative in front of the fraction.

$6 = - \frac{81 b}{22} - \frac{243}{484} + 9 b + 9$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = - \frac{81 b}{22} - \frac{243}{484} + 9 b + 9$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = - \frac{81 b}{22} - \frac{243}{484} + 9 b + 9$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.8.1.2

To write $9 b$ as a fraction with a common denominator, multiply by $\frac{22}{22}$ .

$6 = - \frac{81 b}{22} + 9 b \cdot \frac{22}{22} - \frac{243}{484} + 9$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.8.1.3

Combine $9 b$ and $\frac{22}{22}$ .

$6 = - \frac{81 b}{22} + \frac{9 b \cdot 22}{22} - \frac{243}{484} + 9$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.8.1.4

Combine the numerators over the common denominator.

$6 = \frac{- 81 b + 9 b \cdot 22}{22} - \frac{243}{484} + 9$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.8.1.5

Find the common denominator.

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Step 2.3.4.8.1.5.1

Multiply $\frac{- 81 b + 9 b \cdot 22}{22}$ by $\frac{22}{22}$ .

$6 = \frac{- 81 b + 9 b \cdot 22}{22} \cdot \frac{22}{22} - \frac{243}{484} + 9$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.8.1.5.2

Multiply $\frac{- 81 b + 9 b \cdot 22}{22}$ by $\frac{22}{22}$ .

$6 = \frac{(- 81 b + 9 b \cdot 22) \cdot 22}{22 \cdot 22} - \frac{243}{484} + 9$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.8.1.5.3

Write $9$ as a fraction with denominator $1$ .

$6 = \frac{(- 81 b + 9 b \cdot 22) \cdot 22}{22 \cdot 22} - \frac{243}{484} + \frac{9}{1}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.8.1.5.4

Multiply $\frac{9}{1}$ by $\frac{484}{484}$ .

$6 = \frac{(- 81 b + 9 b \cdot 22) \cdot 22}{22 \cdot 22} - \frac{243}{484} + \frac{9}{1} \cdot \frac{484}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.8.1.5.5

Multiply $\frac{9}{1}$ by $\frac{484}{484}$ .

$6 = \frac{(- 81 b + 9 b \cdot 22) \cdot 22}{22 \cdot 22} - \frac{243}{484} + \frac{9 \cdot 484}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.8.1.5.6

Multiply $22$ by $22$ .

$6 = \frac{(- 81 b + 9 b \cdot 22) \cdot 22}{484} - \frac{243}{484} + \frac{9 \cdot 484}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = \frac{(- 81 b + 9 b \cdot 22) \cdot 22}{484} - \frac{243}{484} + \frac{9 \cdot 484}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.8.1.6

Combine the numerators over the common denominator.

$6 = \frac{(- 81 b + 9 b \cdot 22) \cdot 22 - 243 + 9 \cdot 484}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.8.1.7

Simplify each term.

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Step 2.3.4.8.1.7.1

Multiply $22$ by $9$ .

$6 = \frac{(- 81 b + 198 b) \cdot 22 - 243 + 9 \cdot 484}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.8.1.7.2

Add $- 81 b$ and $198 b$ .

$6 = \frac{117 b \cdot 22 - 243 + 9 \cdot 484}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.8.1.7.3

Multiply $22$ by $117$ .

$6 = \frac{2574 b - 243 + 9 \cdot 484}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.8.1.7.4

Multiply $9$ by $484$ .

$6 = \frac{2574 b - 243 + 4356}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = \frac{2574 b - 243 + 4356}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.8.1.8

Simplify with factoring out.

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Step 2.3.4.8.1.8.1

Add $- 243$ and $4356$ .

$6 = \frac{2574 b + 4113}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.8.1.8.2

Factor $9$ out of $2574 b + 4113$ .

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Step 2.3.4.8.1.8.2.1

Factor $9$ out of $2574 b$ .

$6 = \frac{9 (286 b) + 4113}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.8.1.8.2.2

Factor $9$ out of $4113$ .

$6 = \frac{9 (286 b) + 9 (457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.8.1.8.2.3

Factor $9$ out of $9 (286 b) + 9 (457)$ .

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 36 a + 6 b + 9$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.9

Replace all occurrences of $a$ in $7 = 36 a + 6 b + 9$ with $- \frac{b}{22} - \frac{3}{484}$ .

$7 = 36 (- \frac{b}{22} - \frac{3}{484}) + 6 b + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10

Simplify the right side.

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Step 2.3.4.10.1

Simplify $36 (- \frac{b}{22} - \frac{3}{484}) + 6 b + 9$ .

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Step 2.3.4.10.1.1

Simplify each term.

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Step 2.3.4.10.1.1.1

Apply the distributive property.

$7 = 36 (- \frac{b}{22}) + 36 (- \frac{3}{484}) + 6 b + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.1.2

Cancel the common factor of $2$ .

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Step 2.3.4.10.1.1.2.1

Move the leading negative in $- \frac{b}{22}$ into the numerator.

$7 = 36 (\frac{- b}{22}) + 36 (- \frac{3}{484}) + 6 b + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.1.2.2

Factor $2$ out of $36$ .

$7 = 2 (18) (\frac{- b}{22}) + 36 (- \frac{3}{484}) + 6 b + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.1.2.3

Factor $2$ out of $22$ .

$7 = 2 \cdot (18 (\frac{- b}{2 \cdot 11})) + 36 (- \frac{3}{484}) + 6 b + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.1.2.4

Cancel the common factor.

$7 = 2 \cdot (18 (\frac{- b}{2 \cdot 11})) + 36 (- \frac{3}{484}) + 6 b + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.1.2.5

Rewrite the expression.

$7 = 18 (\frac{- b}{11}) + 36 (- \frac{3}{484}) + 6 b + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = 18 (\frac{- b}{11}) + 36 (- \frac{3}{484}) + 6 b + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.1.3

Combine $18$ and $\frac{- b}{11}$ .

$7 = \frac{18 (- b)}{11} + 36 (- \frac{3}{484}) + 6 b + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.1.4

Multiply $- 1$ by $18$ .

$7 = \frac{- 18 b}{11} + 36 (- \frac{3}{484}) + 6 b + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.1.5

Cancel the common factor of $4$ .

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Step 2.3.4.10.1.1.5.1

Move the leading negative in $- \frac{3}{484}$ into the numerator.

$7 = \frac{- 18 b}{11} + 36 (\frac{- 3}{484}) + 6 b + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.1.5.2

Factor $4$ out of $36$ .

$7 = \frac{- 18 b}{11} + 4 (9) (\frac{- 3}{484}) + 6 b + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.1.5.3

Factor $4$ out of $484$ .

$7 = \frac{- 18 b}{11} + 4 \cdot (9 (\frac{- 3}{4 \cdot 121})) + 6 b + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.1.5.4

Cancel the common factor.

$7 = \frac{- 18 b}{11} + 4 \cdot (9 (\frac{- 3}{4 \cdot 121})) + 6 b + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.1.5.5

Rewrite the expression.

$7 = \frac{- 18 b}{11} + 9 (\frac{- 3}{121}) + 6 b + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = \frac{- 18 b}{11} + 9 (\frac{- 3}{121}) + 6 b + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.1.6

Combine $9$ and $\frac{- 3}{121}$ .

$7 = \frac{- 18 b}{11} + \frac{9 \cdot - 3}{121} + 6 b + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.1.7

Multiply $9$ by $- 3$ .

$7 = \frac{- 18 b}{11} + \frac{- 27}{121} + 6 b + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.1.8

Simplify each term.

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Step 2.3.4.10.1.1.8.1

Move the negative in front of the fraction.

$7 = - \frac{18 b}{11} + \frac{- 27}{121} + 6 b + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.1.8.2

Move the negative in front of the fraction.

$7 = - \frac{18 b}{11} - \frac{27}{121} + 6 b + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = - \frac{18 b}{11} - \frac{27}{121} + 6 b + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = - \frac{18 b}{11} - \frac{27}{121} + 6 b + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.2

To write $6 b$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$7 = - \frac{18 b}{11} + 6 b \cdot \frac{11}{11} - \frac{27}{121} + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.3

Combine $6 b$ and $\frac{11}{11}$ .

$7 = - \frac{18 b}{11} + \frac{6 b \cdot 11}{11} - \frac{27}{121} + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.4

Combine the numerators over the common denominator.

$7 = \frac{- 18 b + 6 b \cdot 11}{11} - \frac{27}{121} + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.5

Find the common denominator.

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Step 2.3.4.10.1.5.1

Multiply $\frac{- 18 b + 6 b \cdot 11}{11}$ by $\frac{11}{11}$ .

$7 = \frac{- 18 b + 6 b \cdot 11}{11} \cdot \frac{11}{11} - \frac{27}{121} + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.5.2

Multiply $\frac{- 18 b + 6 b \cdot 11}{11}$ by $\frac{11}{11}$ .

$7 = \frac{(- 18 b + 6 b \cdot 11) \cdot 11}{11 \cdot 11} - \frac{27}{121} + 9$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.5.3

Write $9$ as a fraction with denominator $1$ .

$7 = \frac{(- 18 b + 6 b \cdot 11) \cdot 11}{11 \cdot 11} - \frac{27}{121} + \frac{9}{1}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.5.4

Multiply $\frac{9}{1}$ by $\frac{121}{121}$ .

$7 = \frac{(- 18 b + 6 b \cdot 11) \cdot 11}{11 \cdot 11} - \frac{27}{121} + \frac{9}{1} \cdot \frac{121}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.5.5

Multiply $\frac{9}{1}$ by $\frac{121}{121}$ .

$7 = \frac{(- 18 b + 6 b \cdot 11) \cdot 11}{11 \cdot 11} - \frac{27}{121} + \frac{9 \cdot 121}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.5.6

Multiply $11$ by $11$ .

$7 = \frac{(- 18 b + 6 b \cdot 11) \cdot 11}{121} - \frac{27}{121} + \frac{9 \cdot 121}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = \frac{(- 18 b + 6 b \cdot 11) \cdot 11}{121} - \frac{27}{121} + \frac{9 \cdot 121}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.6

Combine the numerators over the common denominator.

$7 = \frac{(- 18 b + 6 b \cdot 11) \cdot 11 - 27 + 9 \cdot 121}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.7

Simplify each term.

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Step 2.3.4.10.1.7.1

Multiply $11$ by $6$ .

$7 = \frac{(- 18 b + 66 b) \cdot 11 - 27 + 9 \cdot 121}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.7.2

Add $- 18 b$ and $66 b$ .

$7 = \frac{48 b \cdot 11 - 27 + 9 \cdot 121}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.7.3

Multiply $11$ by $48$ .

$7 = \frac{528 b - 27 + 9 \cdot 121}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.7.4

Multiply $9$ by $121$ .

$7 = \frac{528 b - 27 + 1089}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = \frac{528 b - 27 + 1089}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.8

Simplify with factoring out.

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Step 2.3.4.10.1.8.1

Add $- 27$ and $1089$ .

$7 = \frac{528 b + 1062}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.8.2

Factor $6$ out of $528 b + 1062$ .

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Step 2.3.4.10.1.8.2.1

Factor $6$ out of $528 b$ .

$7 = \frac{6 (88 b) + 1062}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.8.2.2

Factor $6$ out of $1062$ .

$7 = \frac{6 (88 b) + 6 (177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.10.1.8.2.3

Factor $6$ out of $6 (88 b) + 6 (177)$ .

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$7 = 25 a + 5 b + 9$

$c = 9$

Step 2.3.4.11

Replace all occurrences of $a$ in $7 = 25 a + 5 b + 9$ with $- \frac{b}{22} - \frac{3}{484}$ .

$7 = 25 (- \frac{b}{22} - \frac{3}{484}) + 5 b + 9$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.4.12

Simplify the right side.

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Step 2.3.4.12.1

Simplify $25 (- \frac{b}{22} - \frac{3}{484}) + 5 b + 9$ .

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Step 2.3.4.12.1.1

Simplify each term.

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Step 2.3.4.12.1.1.1

Apply the distributive property.

$7 = 25 (- \frac{b}{22}) + 25 (- \frac{3}{484}) + 5 b + 9$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.4.12.1.1.2

Multiply $25 (- \frac{b}{22})$ .

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Step 2.3.4.12.1.1.2.1

Multiply $- 1$ by $25$ .

$7 = - 25 \frac{b}{22} + 25 (- \frac{3}{484}) + 5 b + 9$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.4.12.1.1.2.2

Combine $- 25$ and $\frac{b}{22}$ .

$7 = \frac{- 25 b}{22} + 25 (- \frac{3}{484}) + 5 b + 9$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$7 = \frac{- 25 b}{22} + 25 (- \frac{3}{484}) + 5 b + 9$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.4.12.1.1.3

Multiply $25 (- \frac{3}{484})$ .

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Step 2.3.4.12.1.1.3.1

Multiply $- 1$ by $25$ .

$7 = \frac{- 25 b}{22} - 25 (\frac{3}{484}) + 5 b + 9$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.4.12.1.1.3.2

Combine $- 25$ and $\frac{3}{484}$ .

$7 = \frac{- 25 b}{22} + \frac{- 25 \cdot 3}{484} + 5 b + 9$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.4.12.1.1.3.3

Multiply $- 25$ by $3$ .

$7 = \frac{- 25 b}{22} + \frac{- 75}{484} + 5 b + 9$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$7 = \frac{- 25 b}{22} + \frac{- 75}{484} + 5 b + 9$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.4.12.1.1.4

Simplify each term.

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Step 2.3.4.12.1.1.4.1

Move the negative in front of the fraction.

$7 = - \frac{25 b}{22} + \frac{- 75}{484} + 5 b + 9$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.4.12.1.1.4.2

Move the negative in front of the fraction.

$7 = - \frac{25 b}{22} - \frac{75}{484} + 5 b + 9$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$7 = - \frac{25 b}{22} - \frac{75}{484} + 5 b + 9$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$7 = - \frac{25 b}{22} - \frac{75}{484} + 5 b + 9$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.4.12.1.2

To write $5 b$ as a fraction with a common denominator, multiply by $\frac{22}{22}$ .

$7 = - \frac{25 b}{22} + 5 b \cdot \frac{22}{22} - \frac{75}{484} + 9$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.4.12.1.3

Combine $5 b$ and $\frac{22}{22}$ .

$7 = - \frac{25 b}{22} + \frac{5 b \cdot 22}{22} - \frac{75}{484} + 9$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.4.12.1.4

Combine the numerators over the common denominator.

$7 = \frac{- 25 b + 5 b \cdot 22}{22} - \frac{75}{484} + 9$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.4.12.1.5

Find the common denominator.

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Step 2.3.4.12.1.5.1

Multiply $\frac{- 25 b + 5 b \cdot 22}{22}$ by $\frac{22}{22}$ .

$7 = \frac{- 25 b + 5 b \cdot 22}{22} \cdot \frac{22}{22} - \frac{75}{484} + 9$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.4.12.1.5.2

Multiply $\frac{- 25 b + 5 b \cdot 22}{22}$ by $\frac{22}{22}$ .

$7 = \frac{(- 25 b + 5 b \cdot 22) \cdot 22}{22 \cdot 22} - \frac{75}{484} + 9$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.4.12.1.5.3

Write $9$ as a fraction with denominator $1$ .

$7 = \frac{(- 25 b + 5 b \cdot 22) \cdot 22}{22 \cdot 22} - \frac{75}{484} + \frac{9}{1}$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.4.12.1.5.4

Multiply $\frac{9}{1}$ by $\frac{484}{484}$ .

$7 = \frac{(- 25 b + 5 b \cdot 22) \cdot 22}{22 \cdot 22} - \frac{75}{484} + \frac{9}{1} \cdot \frac{484}{484}$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.4.12.1.5.5

Multiply $\frac{9}{1}$ by $\frac{484}{484}$ .

$7 = \frac{(- 25 b + 5 b \cdot 22) \cdot 22}{22 \cdot 22} - \frac{75}{484} + \frac{9 \cdot 484}{484}$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.4.12.1.5.6

Multiply $22$ by $22$ .

$7 = \frac{(- 25 b + 5 b \cdot 22) \cdot 22}{484} - \frac{75}{484} + \frac{9 \cdot 484}{484}$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$7 = \frac{(- 25 b + 5 b \cdot 22) \cdot 22}{484} - \frac{75}{484} + \frac{9 \cdot 484}{484}$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.4.12.1.6

Combine the numerators over the common denominator.

$7 = \frac{(- 25 b + 5 b \cdot 22) \cdot 22 - 75 + 9 \cdot 484}{484}$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.4.12.1.7

Simplify each term.

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Step 2.3.4.12.1.7.1

Multiply $22$ by $5$ .

$7 = \frac{(- 25 b + 110 b) \cdot 22 - 75 + 9 \cdot 484}{484}$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.4.12.1.7.2

Add $- 25 b$ and $110 b$ .

$7 = \frac{85 b \cdot 22 - 75 + 9 \cdot 484}{484}$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.4.12.1.7.3

Multiply $22$ by $85$ .

$7 = \frac{1870 b - 75 + 9 \cdot 484}{484}$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.4.12.1.7.4

Multiply $9$ by $484$ .

$7 = \frac{1870 b - 75 + 4356}{484}$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$7 = \frac{1870 b - 75 + 4356}{484}$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.4.12.1.8

Add $- 75$ and $4356$ .

$7 = \frac{1870 b + 4281}{484}$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$7 = \frac{1870 b + 4281}{484}$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$7 = \frac{1870 b + 4281}{484}$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$7 = \frac{1870 b + 4281}{484}$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.5

Solve for $b$ in $7 = \frac{1870 b + 4281}{484}$ .

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Step 2.3.5.1

Rewrite the equation as $\frac{1870 b + 4281}{484} = 7$ .

$\frac{1870 b + 4281}{484} = 7$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.5.2

Multiply both sides by $484$ .

$\frac{1870 b + 4281}{484} \cdot 484 = 7 \cdot 484$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.5.3

Simplify.

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Step 2.3.5.3.1

Simplify the left side.

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Step 2.3.5.3.1.1

Cancel the common factor of $484$ .

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Step 2.3.5.3.1.1.1

Cancel the common factor.

$\frac{1870 b + 4281}{484} \cdot 484 = 7 \cdot 484$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.5.3.1.1.2

Rewrite the expression.

$1870 b + 4281 = 7 \cdot 484$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$1870 b + 4281 = 7 \cdot 484$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$1870 b + 4281 = 7 \cdot 484$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.5.3.2

Simplify the right side.

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Step 2.3.5.3.2.1

Multiply $7$ by $484$ .

$1870 b + 4281 = 3388$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$1870 b + 4281 = 3388$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$1870 b + 4281 = 3388$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.5.4

Solve for $b$ .

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Step 2.3.5.4.1

Move all terms not containing $b$ to the right side of the equation.

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Step 2.3.5.4.1.1

Subtract $4281$ from both sides of the equation.

$1870 b = 3388 - 4281$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.5.4.1.2

Subtract $4281$ from $3388$ .

$1870 b = - 893$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$1870 b = - 893$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.5.4.2

Divide each term in $1870 b = - 893$ by $1870$ and simplify.

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Step 2.3.5.4.2.1

Divide each term in $1870 b = - 893$ by $1870$ .

$\frac{1870 b}{1870} = \frac{- 893}{1870}$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.5.4.2.2

Simplify the left side.

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Step 2.3.5.4.2.2.1

Cancel the common factor of $1870$ .

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Step 2.3.5.4.2.2.1.1

Cancel the common factor.

$\frac{1870 b}{1870} = \frac{- 893}{1870}$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.5.4.2.2.1.2

Divide $b$ by $1$ .

$b = \frac{- 893}{1870}$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$b = \frac{- 893}{1870}$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$b = \frac{- 893}{1870}$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.5.4.2.3

Simplify the right side.

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Step 2.3.5.4.2.3.1

Move the negative in front of the fraction.

$b = - \frac{893}{1870}$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$b = - \frac{893}{1870}$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$b = - \frac{893}{1870}$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$b = - \frac{893}{1870}$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$b = - \frac{893}{1870}$

$7 = \frac{6 (88 b + 177)}{121}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6

Replace all occurrences of $b$ with $- \frac{893}{1870}$ in each equation.

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Step 2.3.6.1

Replace all occurrences of $b$ in $7 = \frac{6 (88 b + 177)}{121}$ with $- \frac{893}{1870}$ .

$7 = \frac{6 (88 (- \frac{893}{1870}) + 177)}{121}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.2

Simplify the right side.

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Step 2.3.6.2.1

Simplify $\frac{6 (88 (- \frac{893}{1870}) + 177)}{121}$ .

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Step 2.3.6.2.1.1

Simplify the numerator.

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Step 2.3.6.2.1.1.1

Cancel the common factor of $22$ .

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Step 2.3.6.2.1.1.1.1

Move the leading negative in $- \frac{893}{1870}$ into the numerator.

$7 = \frac{6 (88 (\frac{- 893}{1870}) + 177)}{121}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.2.1.1.1.2

Factor $22$ out of $88$ .

$7 = \frac{6 (22 (4) (\frac{- 893}{1870}) + 177)}{121}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.2.1.1.1.3

Factor $22$ out of $1870$ .

$7 = \frac{6 (22 \cdot (4 (\frac{- 893}{22 \cdot 85})) + 177)}{121}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.2.1.1.1.4

Cancel the common factor.

$7 = \frac{6 (22 \cdot (4 (\frac{- 893}{22 \cdot 85})) + 177)}{121}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.2.1.1.1.5

Rewrite the expression.

$7 = \frac{6 (4 (\frac{- 893}{85}) + 177)}{121}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$7 = \frac{6 (4 (\frac{- 893}{85}) + 177)}{121}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.2.1.1.2

Combine $4$ and $\frac{- 893}{85}$ .

$7 = \frac{6 (\frac{4 \cdot - 893}{85} + 177)}{121}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.2.1.1.3

Multiply $4$ by $- 893$ .

$7 = \frac{6 (\frac{- 3572}{85} + 177)}{121}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.2.1.1.4

Move the negative in front of the fraction.

$7 = \frac{6 (- \frac{3572}{85} + 177)}{121}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.2.1.1.5

To write $177$ as a fraction with a common denominator, multiply by $\frac{85}{85}$ .

$7 = \frac{6 (- \frac{3572}{85} + 177 \cdot \frac{85}{85})}{121}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.2.1.1.6

Combine $177$ and $\frac{85}{85}$ .

$7 = \frac{6 (- \frac{3572}{85} + \frac{177 \cdot 85}{85})}{121}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.2.1.1.7

Combine the numerators over the common denominator.

$7 = \frac{6 (\frac{- 3572 + 177 \cdot 85}{85})}{121}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.2.1.1.8

Simplify the numerator.

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Step 2.3.6.2.1.1.8.1

Multiply $177$ by $85$ .

$7 = \frac{6 (\frac{- 3572 + 15045}{85})}{121}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.2.1.1.8.2

Add $- 3572$ and $15045$ .

$7 = \frac{6 (\frac{11473}{85})}{121}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$7 = \frac{6 (\frac{11473}{85})}{121}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$7 = \frac{6 (\frac{11473}{85})}{121}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.2.1.2

Combine fractions.

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Step 2.3.6.2.1.2.1

Combine $6$ and $\frac{11473}{85}$ .

$7 = \frac{\frac{6 \cdot 11473}{85}}{121}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.2.1.2.2

Multiply $6$ by $11473$ .

$7 = \frac{\frac{68838}{85}}{121}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$7 = \frac{\frac{68838}{85}}{121}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.2.1.3

Multiply the numerator by the reciprocal of the denominator.

$7 = \frac{68838}{85} \cdot \frac{1}{121}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.2.1.4

Cancel the common factor of $11$ .

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Step 2.3.6.2.1.4.1

Factor $11$ out of $68838$ .

$7 = \frac{11 (6258)}{85} \cdot \frac{1}{121}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.2.1.4.2

Factor $11$ out of $121$ .

$7 = \frac{11 \cdot 6258}{85} \cdot \frac{1}{11 \cdot 11}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.2.1.4.3

Cancel the common factor.

$7 = \frac{11 \cdot 6258}{85} \cdot \frac{1}{11 \cdot 11}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.2.1.4.4

Rewrite the expression.

$7 = \frac{6258}{85} \cdot \frac{1}{11}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$7 = \frac{6258}{85} \cdot \frac{1}{11}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.2.1.5

Multiply $\frac{6258}{85}$ by $\frac{1}{11}$ .

$7 = \frac{6258}{85 \cdot 11}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.2.1.6

Multiply $85$ by $11$ .

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$6 = \frac{9 (286 b + 457)}{484}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.3

Replace all occurrences of $b$ in $6 = \frac{9 (286 b + 457)}{484}$ with $- \frac{893}{1870}$ .

$6 = \frac{9 (286 (- \frac{893}{1870}) + 457)}{484}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.4

Simplify the right side.

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Step 2.3.6.4.1

Simplify $\frac{9 (286 (- \frac{893}{1870}) + 457)}{484}$ .

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Step 2.3.6.4.1.1

Simplify the numerator.

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Step 2.3.6.4.1.1.1

Cancel the common factor of $22$ .

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Step 2.3.6.4.1.1.1.1

Move the leading negative in $- \frac{893}{1870}$ into the numerator.

$6 = \frac{9 (286 (\frac{- 893}{1870}) + 457)}{484}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.4.1.1.1.2

Factor $22$ out of $286$ .

$6 = \frac{9 (22 (13) (\frac{- 893}{1870}) + 457)}{484}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.4.1.1.1.3

Factor $22$ out of $1870$ .

$6 = \frac{9 (22 \cdot (13 (\frac{- 893}{22 \cdot 85})) + 457)}{484}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.4.1.1.1.4

Cancel the common factor.

$6 = \frac{9 (22 \cdot (13 (\frac{- 893}{22 \cdot 85})) + 457)}{484}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.4.1.1.1.5

Rewrite the expression.

$6 = \frac{9 (13 (\frac{- 893}{85}) + 457)}{484}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$6 = \frac{9 (13 (\frac{- 893}{85}) + 457)}{484}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.4.1.1.2

Combine $13$ and $\frac{- 893}{85}$ .

$6 = \frac{9 (\frac{13 \cdot - 893}{85} + 457)}{484}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.4.1.1.3

Multiply $13$ by $- 893$ .

$6 = \frac{9 (\frac{- 11609}{85} + 457)}{484}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.4.1.1.4

Move the negative in front of the fraction.

$6 = \frac{9 (- \frac{11609}{85} + 457)}{484}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.4.1.1.5

To write $457$ as a fraction with a common denominator, multiply by $\frac{85}{85}$ .

$6 = \frac{9 (- \frac{11609}{85} + 457 \cdot \frac{85}{85})}{484}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.4.1.1.6

Combine $457$ and $\frac{85}{85}$ .

$6 = \frac{9 (- \frac{11609}{85} + \frac{457 \cdot 85}{85})}{484}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.4.1.1.7

Combine the numerators over the common denominator.

$6 = \frac{9 (\frac{- 11609 + 457 \cdot 85}{85})}{484}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.4.1.1.8

Simplify the numerator.

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Step 2.3.6.4.1.1.8.1

Multiply $457$ by $85$ .

$6 = \frac{9 (\frac{- 11609 + 38845}{85})}{484}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.4.1.1.8.2

Add $- 11609$ and $38845$ .

$6 = \frac{9 (\frac{27236}{85})}{484}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$6 = \frac{9 (\frac{27236}{85})}{484}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$6 = \frac{9 (\frac{27236}{85})}{484}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.4.1.2

Combine fractions.

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Step 2.3.6.4.1.2.1

Combine $9$ and $\frac{27236}{85}$ .

$6 = \frac{\frac{9 \cdot 27236}{85}}{484}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.4.1.2.2

Multiply $9$ by $27236$ .

$6 = \frac{\frac{245124}{85}}{484}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$6 = \frac{\frac{245124}{85}}{484}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.4.1.3

Multiply the numerator by the reciprocal of the denominator.

$6 = \frac{245124}{85} \cdot \frac{1}{484}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.4.1.4

Cancel the common factor of $44$ .

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Step 2.3.6.4.1.4.1

Factor $44$ out of $245124$ .

$6 = \frac{44 (5571)}{85} \cdot \frac{1}{484}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.4.1.4.2

Factor $44$ out of $484$ .

$6 = \frac{44 \cdot 5571}{85} \cdot \frac{1}{44 \cdot 11}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.4.1.4.3

Cancel the common factor.

$6 = \frac{44 \cdot 5571}{85} \cdot \frac{1}{44 \cdot 11}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.4.1.4.4

Rewrite the expression.

$6 = \frac{5571}{85} \cdot \frac{1}{11}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$6 = \frac{5571}{85} \cdot \frac{1}{11}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.4.1.5

Multiply $\frac{5571}{85}$ by $\frac{1}{11}$ .

$6 = \frac{5571}{85 \cdot 11}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.4.1.6

Multiply $85$ by $11$ .

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$9 = \frac{3 (858 b + 1283)}{484}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.5

Replace all occurrences of $b$ in $9 = \frac{3 (858 b + 1283)}{484}$ with $- \frac{893}{1870}$ .

$9 = \frac{3 (858 (- \frac{893}{1870}) + 1283)}{484}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.6

Simplify the right side.

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Step 2.3.6.6.1

Simplify $\frac{3 (858 (- \frac{893}{1870}) + 1283)}{484}$ .

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Step 2.3.6.6.1.1

Simplify the numerator.

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Step 2.3.6.6.1.1.1

Cancel the common factor of $22$ .

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Step 2.3.6.6.1.1.1.1

Move the leading negative in $- \frac{893}{1870}$ into the numerator.

$9 = \frac{3 (858 (\frac{- 893}{1870}) + 1283)}{484}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.6.1.1.1.2

Factor $22$ out of $858$ .

$9 = \frac{3 (22 (39) (\frac{- 893}{1870}) + 1283)}{484}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.6.1.1.1.3

Factor $22$ out of $1870$ .

$9 = \frac{3 (22 \cdot (39 (\frac{- 893}{22 \cdot 85})) + 1283)}{484}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.6.1.1.1.4

Cancel the common factor.

$9 = \frac{3 (22 \cdot (39 (\frac{- 893}{22 \cdot 85})) + 1283)}{484}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.6.1.1.1.5

Rewrite the expression.

$9 = \frac{3 (39 (\frac{- 893}{85}) + 1283)}{484}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$9 = \frac{3 (39 (\frac{- 893}{85}) + 1283)}{484}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.6.1.1.2

Combine $39$ and $\frac{- 893}{85}$ .

$9 = \frac{3 (\frac{39 \cdot - 893}{85} + 1283)}{484}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.6.1.1.3

Multiply $39$ by $- 893$ .

$9 = \frac{3 (\frac{- 34827}{85} + 1283)}{484}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.6.1.1.4

Move the negative in front of the fraction.

$9 = \frac{3 (- \frac{34827}{85} + 1283)}{484}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.6.1.1.5

To write $1283$ as a fraction with a common denominator, multiply by $\frac{85}{85}$ .

$9 = \frac{3 (- \frac{34827}{85} + 1283 \cdot \frac{85}{85})}{484}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.6.1.1.6

Combine $1283$ and $\frac{85}{85}$ .

$9 = \frac{3 (- \frac{34827}{85} + \frac{1283 \cdot 85}{85})}{484}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.6.1.1.7

Combine the numerators over the common denominator.

$9 = \frac{3 (\frac{- 34827 + 1283 \cdot 85}{85})}{484}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.6.1.1.8

Simplify the numerator.

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Step 2.3.6.6.1.1.8.1

Multiply $1283$ by $85$ .

$9 = \frac{3 (\frac{- 34827 + 109055}{85})}{484}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.6.1.1.8.2

Add $- 34827$ and $109055$ .

$9 = \frac{3 (\frac{74228}{85})}{484}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$9 = \frac{3 (\frac{74228}{85})}{484}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$9 = \frac{3 (\frac{74228}{85})}{484}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.6.1.2

Combine fractions.

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Step 2.3.6.6.1.2.1

Combine $3$ and $\frac{74228}{85}$ .

$9 = \frac{\frac{3 \cdot 74228}{85}}{484}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.6.1.2.2

Multiply $3$ by $74228$ .

$9 = \frac{\frac{222684}{85}}{484}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$9 = \frac{\frac{222684}{85}}{484}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.6.1.3

Multiply the numerator by the reciprocal of the denominator.

$9 = \frac{222684}{85} \cdot \frac{1}{484}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.6.1.4

Cancel the common factor of $44$ .

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Step 2.3.6.6.1.4.1

Factor $44$ out of $222684$ .

$9 = \frac{44 (5061)}{85} \cdot \frac{1}{484}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.6.1.4.2

Factor $44$ out of $484$ .

$9 = \frac{44 \cdot 5061}{85} \cdot \frac{1}{44 \cdot 11}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.6.1.4.3

Cancel the common factor.

$9 = \frac{44 \cdot 5061}{85} \cdot \frac{1}{44 \cdot 11}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.6.1.4.4

Rewrite the expression.

$9 = \frac{5061}{85} \cdot \frac{1}{11}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$9 = \frac{5061}{85} \cdot \frac{1}{11}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.6.1.5

Multiply $\frac{5061}{85}$ by $\frac{1}{11}$ .

$9 = \frac{5061}{85 \cdot 11}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.6.1.6

Multiply $85$ by $11$ .

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$7 = \frac{3 (176 b + 299)}{121}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.7

Replace all occurrences of $b$ in $7 = \frac{3 (176 b + 299)}{121}$ with $- \frac{893}{1870}$ .

$7 = \frac{3 (176 (- \frac{893}{1870}) + 299)}{121}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.8

Simplify the right side.

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Step 2.3.6.8.1

Simplify $\frac{3 (176 (- \frac{893}{1870}) + 299)}{121}$ .

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Step 2.3.6.8.1.1

Simplify the numerator.

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Step 2.3.6.8.1.1.1

Cancel the common factor of $22$ .

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Step 2.3.6.8.1.1.1.1

Move the leading negative in $- \frac{893}{1870}$ into the numerator.

$7 = \frac{3 (176 (\frac{- 893}{1870}) + 299)}{121}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.8.1.1.1.2

Factor $22$ out of $176$ .

$7 = \frac{3 (22 (8) (\frac{- 893}{1870}) + 299)}{121}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.8.1.1.1.3

Factor $22$ out of $1870$ .

$7 = \frac{3 (22 \cdot (8 (\frac{- 893}{22 \cdot 85})) + 299)}{121}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.8.1.1.1.4

Cancel the common factor.

$7 = \frac{3 (22 \cdot (8 (\frac{- 893}{22 \cdot 85})) + 299)}{121}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.8.1.1.1.5

Rewrite the expression.

$7 = \frac{3 (8 (\frac{- 893}{85}) + 299)}{121}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$7 = \frac{3 (8 (\frac{- 893}{85}) + 299)}{121}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.8.1.1.2

Combine $8$ and $\frac{- 893}{85}$ .

$7 = \frac{3 (\frac{8 \cdot - 893}{85} + 299)}{121}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.8.1.1.3

Multiply $8$ by $- 893$ .

$7 = \frac{3 (\frac{- 7144}{85} + 299)}{121}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.8.1.1.4

Move the negative in front of the fraction.

$7 = \frac{3 (- \frac{7144}{85} + 299)}{121}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.8.1.1.5

To write $299$ as a fraction with a common denominator, multiply by $\frac{85}{85}$ .

$7 = \frac{3 (- \frac{7144}{85} + 299 \cdot \frac{85}{85})}{121}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.8.1.1.6

Combine $299$ and $\frac{85}{85}$ .

$7 = \frac{3 (- \frac{7144}{85} + \frac{299 \cdot 85}{85})}{121}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.8.1.1.7

Combine the numerators over the common denominator.

$7 = \frac{3 (\frac{- 7144 + 299 \cdot 85}{85})}{121}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.8.1.1.8

Simplify the numerator.

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Step 2.3.6.8.1.1.8.1

Multiply $299$ by $85$ .

$7 = \frac{3 (\frac{- 7144 + 25415}{85})}{121}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.8.1.1.8.2

Add $- 7144$ and $25415$ .

$7 = \frac{3 (\frac{18271}{85})}{121}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$7 = \frac{3 (\frac{18271}{85})}{121}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$7 = \frac{3 (\frac{18271}{85})}{121}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.8.1.2

Combine fractions.

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Step 2.3.6.8.1.2.1

Combine $3$ and $\frac{18271}{85}$ .

$7 = \frac{\frac{3 \cdot 18271}{85}}{121}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.8.1.2.2

Multiply $3$ by $18271$ .

$7 = \frac{\frac{54813}{85}}{121}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$7 = \frac{\frac{54813}{85}}{121}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.8.1.3

Multiply the numerator by the reciprocal of the denominator.

$7 = \frac{54813}{85} \cdot \frac{1}{121}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.8.1.4

Cancel the common factor of $121$ .

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Step 2.3.6.8.1.4.1

Factor $121$ out of $54813$ .

$7 = \frac{121 (453)}{85} \cdot \frac{1}{121}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.8.1.4.2

Cancel the common factor.

$7 = \frac{121 \cdot 453}{85} \cdot \frac{1}{121}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.8.1.4.3

Rewrite the expression.

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$8 = \frac{3 (418 b + 1091)}{484}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.9

Replace all occurrences of $b$ in $8 = \frac{3 (418 b + 1091)}{484}$ with $- \frac{893}{1870}$ .

$8 = \frac{3 (418 (- \frac{893}{1870}) + 1091)}{484}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.10

Simplify the right side.

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Step 2.3.6.10.1

Simplify $\frac{3 (418 (- \frac{893}{1870}) + 1091)}{484}$ .

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Step 2.3.6.10.1.1

Simplify the numerator.

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Step 2.3.6.10.1.1.1

Cancel the common factor of $22$ .

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Step 2.3.6.10.1.1.1.1

Move the leading negative in $- \frac{893}{1870}$ into the numerator.

$8 = \frac{3 (418 (\frac{- 893}{1870}) + 1091)}{484}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.10.1.1.1.2

Factor $22$ out of $418$ .

$8 = \frac{3 (22 (19) (\frac{- 893}{1870}) + 1091)}{484}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.10.1.1.1.3

Factor $22$ out of $1870$ .

$8 = \frac{3 (22 \cdot (19 (\frac{- 893}{22 \cdot 85})) + 1091)}{484}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.10.1.1.1.4

Cancel the common factor.

$8 = \frac{3 (22 \cdot (19 (\frac{- 893}{22 \cdot 85})) + 1091)}{484}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.10.1.1.1.5

Rewrite the expression.

$8 = \frac{3 (19 (\frac{- 893}{85}) + 1091)}{484}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$8 = \frac{3 (19 (\frac{- 893}{85}) + 1091)}{484}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.10.1.1.2

Combine $19$ and $\frac{- 893}{85}$ .

$8 = \frac{3 (\frac{19 \cdot - 893}{85} + 1091)}{484}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.10.1.1.3

Multiply $19$ by $- 893$ .

$8 = \frac{3 (\frac{- 16967}{85} + 1091)}{484}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.10.1.1.4

Move the negative in front of the fraction.

$8 = \frac{3 (- \frac{16967}{85} + 1091)}{484}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.10.1.1.5

To write $1091$ as a fraction with a common denominator, multiply by $\frac{85}{85}$ .

$8 = \frac{3 (- \frac{16967}{85} + 1091 \cdot \frac{85}{85})}{484}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.10.1.1.6

Combine $1091$ and $\frac{85}{85}$ .

$8 = \frac{3 (- \frac{16967}{85} + \frac{1091 \cdot 85}{85})}{484}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.10.1.1.7

Combine the numerators over the common denominator.

$8 = \frac{3 (\frac{- 16967 + 1091 \cdot 85}{85})}{484}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.10.1.1.8

Simplify the numerator.

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Step 2.3.6.10.1.1.8.1

Multiply $1091$ by $85$ .

$8 = \frac{3 (\frac{- 16967 + 92735}{85})}{484}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.10.1.1.8.2

Add $- 16967$ and $92735$ .

$8 = \frac{3 (\frac{75768}{85})}{484}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$8 = \frac{3 (\frac{75768}{85})}{484}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$8 = \frac{3 (\frac{75768}{85})}{484}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.10.1.2

Combine fractions.

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Step 2.3.6.10.1.2.1

Combine $3$ and $\frac{75768}{85}$ .

$8 = \frac{\frac{3 \cdot 75768}{85}}{484}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.10.1.2.2

Multiply $3$ by $75768$ .

$8 = \frac{\frac{227304}{85}}{484}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$8 = \frac{\frac{227304}{85}}{484}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.10.1.3

Multiply the numerator by the reciprocal of the denominator.

$8 = \frac{227304}{85} \cdot \frac{1}{484}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.10.1.4

Cancel the common factor of $44$ .

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Step 2.3.6.10.1.4.1

Factor $44$ out of $227304$ .

$8 = \frac{44 (5166)}{85} \cdot \frac{1}{484}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.10.1.4.2

Factor $44$ out of $484$ .

$8 = \frac{44 \cdot 5166}{85} \cdot \frac{1}{44 \cdot 11}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.10.1.4.3

Cancel the common factor.

$8 = \frac{44 \cdot 5166}{85} \cdot \frac{1}{44 \cdot 11}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.10.1.4.4

Rewrite the expression.

$8 = \frac{5166}{85} \cdot \frac{1}{11}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$8 = \frac{5166}{85} \cdot \frac{1}{11}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.10.1.5

Multiply $\frac{5166}{85}$ by $\frac{1}{11}$ .

$8 = \frac{5166}{85 \cdot 11}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.10.1.6

Multiply $85$ by $11$ .

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$a = - \frac{b}{22} - \frac{3}{484}$

$c = 9$

Step 2.3.6.11

Replace all occurrences of $b$ in $a = - \frac{b}{22} - \frac{3}{484}$ with $- \frac{893}{1870}$ .

$a = - \frac{- \frac{893}{1870}}{22} - \frac{3}{484}$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$c = 9$

Step 2.3.6.12

Simplify the right side.

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Step 2.3.6.12.1

Simplify $- \frac{- \frac{893}{1870}}{22} - \frac{3}{484}$ .

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Step 2.3.6.12.1.1

Simplify each term.

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Step 2.3.6.12.1.1.1

Multiply the numerator by the reciprocal of the denominator.

$a = - (- \frac{893}{1870} \cdot \frac{1}{22}) - \frac{3}{484}$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$c = 9$

Step 2.3.6.12.1.1.2

Multiply $- \frac{893}{1870} \cdot \frac{1}{22}$ .

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Step 2.3.6.12.1.1.2.1

Multiply $\frac{1}{22}$ by $\frac{893}{1870}$ .

$a = \frac{893}{22 \cdot 1870} - \frac{3}{484}$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$c = 9$

Step 2.3.6.12.1.1.2.2

Multiply $22$ by $1870$ .

$a = \frac{893}{41140} - \frac{3}{484}$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$c = 9$

$a = \frac{893}{41140} - \frac{3}{484}$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$c = 9$

Step 2.3.6.12.1.1.3

Multiply $- - \frac{893}{41140}$ .

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Step 2.3.6.12.1.1.3.1

Multiply $- 1$ by $- 1$ .

$a = 1 (\frac{893}{41140}) - \frac{3}{484}$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$c = 9$

Step 2.3.6.12.1.1.3.2

Multiply $\frac{893}{41140}$ by $1$ .

$a = \frac{893}{41140} - \frac{3}{484}$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$c = 9$

$a = \frac{893}{41140} - \frac{3}{484}$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$c = 9$

$a = \frac{893}{41140} - \frac{3}{484}$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$c = 9$

Step 2.3.6.12.1.2

To write $- \frac{3}{484}$ as a fraction with a common denominator, multiply by $\frac{85}{85}$ .

$a = \frac{893}{41140} - \frac{3}{484} \cdot \frac{85}{85}$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$c = 9$

Step 2.3.6.12.1.3

Write each expression with a common denominator of $41140$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.6.12.1.3.1

Multiply $\frac{3}{484}$ by $\frac{85}{85}$ .

$a = \frac{893}{41140} - \frac{3 \cdot 85}{484 \cdot 85}$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$c = 9$

Step 2.3.6.12.1.3.2

Multiply $484$ by $85$ .

$a = \frac{893}{41140} - \frac{3 \cdot 85}{41140}$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$c = 9$

$a = \frac{893}{41140} - \frac{3 \cdot 85}{41140}$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$c = 9$

Step 2.3.6.12.1.4

Combine the numerators over the common denominator.

$a = \frac{893 - 3 \cdot 85}{41140}$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$c = 9$

Step 2.3.6.12.1.5

Simplify the numerator.

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Step 2.3.6.12.1.5.1

Multiply $- 3$ by $85$ .

$a = \frac{893 - 255}{41140}$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$c = 9$

Step 2.3.6.12.1.5.2

Subtract $255$ from $893$ .

$a = \frac{638}{41140}$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$c = 9$

$a = \frac{638}{41140}$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$c = 9$

Step 2.3.6.12.1.6

Cancel the common factor of $638$ and $41140$ .

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Step 2.3.6.12.1.6.1

Factor $22$ out of $638$ .

$a = \frac{22 (29)}{41140}$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$c = 9$

Step 2.3.6.12.1.6.2

Cancel the common factors.

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Step 2.3.6.12.1.6.2.1

Factor $22$ out of $41140$ .

$a = \frac{22 \cdot 29}{22 \cdot 1870}$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$c = 9$

Step 2.3.6.12.1.6.2.2

Cancel the common factor.

$a = \frac{22 \cdot 29}{22 \cdot 1870}$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$c = 9$

Step 2.3.6.12.1.6.2.3

Rewrite the expression.

$a = \frac{29}{1870}$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$c = 9$

$a = \frac{29}{1870}$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$c = 9$

$a = \frac{29}{1870}$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$c = 9$

$a = \frac{29}{1870}$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$c = 9$

$a = \frac{29}{1870}$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$c = 9$

$a = \frac{29}{1870}$

$8 = \frac{5166}{935}$

$7 = \frac{453}{85}$

$9 = \frac{5061}{935}$

$6 = \frac{5571}{935}$

$7 = \frac{6258}{935}$

$b = - \frac{893}{1870}$

$c = 9$

Step 2.3.7

Since $8 = \frac{5166}{935}$ is not true, there is no solution.

No solution

Step 2.4

Calculate the value of $y$ using each $x$ value in the table and compare this value to the given $y$ value in the table.

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Step 2.4.1

Calculate the value of $y$ such that $y = a x^{2} + b$ when $a = 0$ , $b = 0$ , $c = 0$ , and $x = 0$ .

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Step 2.4.1.1

Simplify each term.

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Step 2.4.1.1.1

Multiply $0$ by ${(0)}^{2}$ by adding the exponents.

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Step 2.4.1.1.1.1

Multiply $0$ by ${(0)}^{2}$ .

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Step 2.4.1.1.1.1.1

Raise $0$ to the power of $1$ .

$y = 0 \cdot {(0)}^{2} + (0) \cdot (0) + 0$

Step 2.4.1.1.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = 0^{1 + 2} + (0) \cdot (0) + 0$

Step 2.4.1.1.1.2

Add $1$ and $2$ .

$y = 0^{3} + (0) \cdot (0) + 0$

Step 2.4.1.1.2

Raising $0$ to any positive power yields $0$ .

$y = 0 + (0) \cdot (0) + 0$

Step 2.4.1.1.3

Multiply $0$ by $0$ .

$y = 0 + 0 + 0$

Step 2.4.1.2

Simplify by adding numbers.

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Step 2.4.1.2.1

Add $0$ and $0$ .

$y = 0 + 0$

Step 2.4.1.2.2

Add $0$ and $0$ .

$y = 0$

Step 2.4.2

If the table has a quadratic function rule, $y = y$ for the corresponding $x$ value, $x = 0$ . This check does not pass, since $y = 0$ and $y = 9$ . The function rule can't be quadratic.

$0 \neq 9$

Step 2.4.3

Since $y \neq y$ for the corresponding $x$ values, the function is not quadratic.

The function is not quadratic

Step 3

Check if the function rule is cubic.

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Step 3.1

To find if the table follows a function rule, check whether the function rule could follow the form $y = a x^{3} + b x^{2} + c x + d$ .

$y = a x^{3} + b x^{2} + c x + d$

Step 3.2

Build a set of $4$ equations from the table such that $y = a x^{3} + b x^{2} + c x + d$ .

Step 3.3

Calculate the values of $a$ , $b$ , $c$ , and $d$ .

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Step 3.3.1

Solve for $d$ in $9 = a \cdot 0^{3} + b \cdot 0^{2} + d$ .

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Step 3.3.1.1

Rewrite the equation as $a \cdot 0^{3} + b \cdot 0^{2} + d = 9$ .

$a \cdot 0^{3} + b \cdot 0^{2} + d = 9$

$7 = a \cdot 5^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 6^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.1.2

Simplify $a \cdot 0^{3} + b \cdot 0^{2} + d$ .

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Step 3.3.1.2.1

Simplify each term.

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Step 3.3.1.2.1.1

Raising $0$ to any positive power yields $0$ .

$a \cdot 0 + b \cdot 0^{2} + d = 9$

$7 = a \cdot 5^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 6^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.1.2.1.2

Multiply $a$ by $0$ .

$0 + b \cdot 0^{2} + d = 9$

$7 = a \cdot 5^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 6^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.1.2.1.3

Raising $0$ to any positive power yields $0$ .

$0 + b \cdot 0 + d = 9$

$7 = a \cdot 5^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 6^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.1.2.1.4

Multiply $b$ by $0$ .

$0 + 0 + d = 9$

$7 = a \cdot 5^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 6^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$0 + 0 + d = 9$

$7 = a \cdot 5^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 6^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.1.2.2

Combine the opposite terms in $0 + 0 + d$ .

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Step 3.3.1.2.2.1

Add $0$ and $0$ .

$0 + d = 9$

$7 = a \cdot 5^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 6^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.1.2.2.2

Add $0$ and $d$ .

$d = 9$

$7 = a \cdot 5^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 6^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$d = 9$

$7 = a \cdot 5^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 6^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$d = 9$

$7 = a \cdot 5^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 6^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$d = 9$

$7 = a \cdot 5^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 6^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2

Replace all occurrences of $d$ with $9$ in each equation.

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Step 3.3.2.1

Replace all occurrences of $d$ in $7 = a \cdot 5^{3} + b \cdot 0^{2} + d$ with $9$ .

$7 = a \cdot 5^{3} + b \cdot 0^{2} + 9$

$d = 9$

$7 = a \cdot 6^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.2

Simplify $7 = a \cdot 5^{3} + b \cdot 0^{2} + 9$ .

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Step 3.3.2.2.1

Simplify the left side.

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Step 3.3.2.2.1.1

Remove parentheses.

$7 = a \cdot 5^{3} + b \cdot 0^{2} + 9$

$d = 9$

$7 = a \cdot 6^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 5^{3} + b \cdot 0^{2} + 9$

$d = 9$

$7 = a \cdot 6^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.2.2

Simplify the right side.

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Step 3.3.2.2.2.1

Simplify $a \cdot 5^{3} + b \cdot 0^{2} + 9$ .

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Step 3.3.2.2.2.1.1

Simplify each term.

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Step 3.3.2.2.2.1.1.1

Raise $5$ to the power of $3$ .

$7 = a \cdot 125 + b \cdot 0^{2} + 9$

$d = 9$

$7 = a \cdot 6^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.2.2.1.1.2

Move $125$ to the left of $a$ .

$7 = 125 \cdot a + b \cdot 0^{2} + 9$

$d = 9$

$7 = a \cdot 6^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.2.2.1.1.3

Raising $0$ to any positive power yields $0$ .

$7 = 125 a + b \cdot 0 + 9$

$d = 9$

$7 = a \cdot 6^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.2.2.1.1.4

Multiply $b$ by $0$ .

$7 = 125 a + 0 + 9$

$d = 9$

$7 = a \cdot 6^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$7 = 125 a + 0 + 9$

$d = 9$

$7 = a \cdot 6^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.2.2.1.2

Add $125 a$ and $0$ .

$7 = 125 a + 9$

$d = 9$

$7 = a \cdot 6^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$7 = 125 a + 9$

$d = 9$

$7 = a \cdot 6^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$7 = 125 a + 9$

$d = 9$

$7 = a \cdot 6^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$7 = 125 a + 9$

$d = 9$

$7 = a \cdot 6^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.3

Replace all occurrences of $d$ in $7 = a \cdot 6^{3} + b \cdot 0^{2} + d$ with $9$ .

$7 = a \cdot 6^{3} + b \cdot 0^{2} + 9$

$7 = 125 a + 9$

$d = 9$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.4

Simplify $7 = a \cdot 6^{3} + b \cdot 0^{2} + 9$ .

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Step 3.3.2.4.1

Simplify the left side.

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Step 3.3.2.4.1.1

Remove parentheses.

$7 = a \cdot 6^{3} + b \cdot 0^{2} + 9$

$7 = 125 a + 9$

$d = 9$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 6^{3} + b \cdot 0^{2} + 9$

$7 = 125 a + 9$

$d = 9$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.4.2

Simplify the right side.

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Step 3.3.2.4.2.1

Simplify $a \cdot 6^{3} + b \cdot 0^{2} + 9$ .

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Step 3.3.2.4.2.1.1

Simplify each term.

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Step 3.3.2.4.2.1.1.1

Raise $6$ to the power of $3$ .

$7 = a \cdot 216 + b \cdot 0^{2} + 9$

$7 = 125 a + 9$

$d = 9$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.4.2.1.1.2

Move $216$ to the left of $a$ .

$7 = 216 \cdot a + b \cdot 0^{2} + 9$

$7 = 125 a + 9$

$d = 9$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.4.2.1.1.3

Raising $0$ to any positive power yields $0$ .

$7 = 216 a + b \cdot 0 + 9$

$7 = 125 a + 9$

$d = 9$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.4.2.1.1.4

Multiply $b$ by $0$ .

$7 = 216 a + 0 + 9$

$7 = 125 a + 9$

$d = 9$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$7 = 216 a + 0 + 9$

$7 = 125 a + 9$

$d = 9$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.4.2.1.2

Add $216 a$ and $0$ .

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.5

Replace all occurrences of $d$ in $6 = a \cdot 9^{3} + b \cdot 0^{2} + d$ with $9$ .

$6 = a \cdot 9^{3} + b \cdot 0^{2} + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.6

Simplify $6 = a \cdot 9^{3} + b \cdot 0^{2} + 9$ .

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Step 3.3.2.6.1

Simplify the left side.

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Step 3.3.2.6.1.1

Remove parentheses.

$6 = a \cdot 9^{3} + b \cdot 0^{2} + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 9^{3} + b \cdot 0^{2} + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.6.2

Simplify the right side.

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Step 3.3.2.6.2.1

Simplify $a \cdot 9^{3} + b \cdot 0^{2} + 9$ .

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Step 3.3.2.6.2.1.1

Simplify each term.

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Step 3.3.2.6.2.1.1.1

Raise $9$ to the power of $3$ .

$6 = a \cdot 729 + b \cdot 0^{2} + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.6.2.1.1.2

Move $729$ to the left of $a$ .

$6 = 729 \cdot a + b \cdot 0^{2} + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.6.2.1.1.3

Raising $0$ to any positive power yields $0$ .

$6 = 729 a + b \cdot 0 + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.6.2.1.1.4

Multiply $b$ by $0$ .

$6 = 729 a + 0 + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$6 = 729 a + 0 + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.6.2.1.2

Add $729 a$ and $0$ .

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.7

Replace all occurrences of $d$ in $9 = a \cdot 13^{3} + b \cdot 0^{2} + d$ with $9$ .

$9 = a \cdot 13^{3} + b \cdot 0^{2} + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.8

Simplify $9 = a \cdot 13^{3} + b \cdot 0^{2} + 9$ .

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Step 3.3.2.8.1

Simplify the left side.

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Step 3.3.2.8.1.1

Remove parentheses.

$9 = a \cdot 13^{3} + b \cdot 0^{2} + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$9 = a \cdot 13^{3} + b \cdot 0^{2} + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.8.2

Simplify the right side.

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Step 3.3.2.8.2.1

Simplify $a \cdot 13^{3} + b \cdot 0^{2} + 9$ .

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Step 3.3.2.8.2.1.1

Simplify each term.

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Step 3.3.2.8.2.1.1.1

Raise $13$ to the power of $3$ .

$9 = a \cdot 2197 + b \cdot 0^{2} + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.8.2.1.1.2

Move $2197$ to the left of $a$ .

$9 = 2197 \cdot a + b \cdot 0^{2} + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.8.2.1.1.3

Raising $0$ to any positive power yields $0$ .

$9 = 2197 a + b \cdot 0 + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.8.2.1.1.4

Multiply $b$ by $0$ .

$9 = 2197 a + 0 + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$9 = 2197 a + 0 + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.8.2.1.2

Add $2197 a$ and $0$ .

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.9

Replace all occurrences of $d$ in $7 = a \cdot 16^{3} + b \cdot 0^{2} + d$ with $9$ .

$7 = a \cdot 16^{3} + b \cdot 0^{2} + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.10

Simplify $7 = a \cdot 16^{3} + b \cdot 0^{2} + 9$ .

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Step 3.3.2.10.1

Simplify the left side.

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Step 3.3.2.10.1.1

Remove parentheses.

$7 = a \cdot 16^{3} + b \cdot 0^{2} + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$7 = a \cdot 16^{3} + b \cdot 0^{2} + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.10.2

Simplify the right side.

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Step 3.3.2.10.2.1

Simplify $a \cdot 16^{3} + b \cdot 0^{2} + 9$ .

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Step 3.3.2.10.2.1.1

Simplify each term.

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Step 3.3.2.10.2.1.1.1

Raise $16$ to the power of $3$ .

$7 = a \cdot 4096 + b \cdot 0^{2} + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.10.2.1.1.2

Move $4096$ to the left of $a$ .

$7 = 4096 \cdot a + b \cdot 0^{2} + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.10.2.1.1.3

Raising $0$ to any positive power yields $0$ .

$7 = 4096 a + b \cdot 0 + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.10.2.1.1.4

Multiply $b$ by $0$ .

$7 = 4096 a + 0 + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$7 = 4096 a + 0 + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.10.2.1.2

Add $4096 a$ and $0$ .

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + d$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.11

Replace all occurrences of $d$ in $8 = a \cdot 19^{3} + b \cdot 0^{2} + d$ with $9$ .

$8 = a \cdot 19^{3} + b \cdot 0^{2} + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.12

Simplify $8 = a \cdot 19^{3} + b \cdot 0^{2} + 9$ .

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Step 3.3.2.12.1

Simplify the left side.

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Step 3.3.2.12.1.1

Remove parentheses.

$8 = a \cdot 19^{3} + b \cdot 0^{2} + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$8 = a \cdot 19^{3} + b \cdot 0^{2} + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.12.2

Simplify the right side.

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Step 3.3.2.12.2.1

Simplify $a \cdot 19^{3} + b \cdot 0^{2} + 9$ .

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Step 3.3.2.12.2.1.1

Simplify each term.

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Step 3.3.2.12.2.1.1.1

Raise $19$ to the power of $3$ .

$8 = a \cdot 6859 + b \cdot 0^{2} + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.12.2.1.1.2

Move $6859$ to the left of $a$ .

$8 = 6859 \cdot a + b \cdot 0^{2} + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.12.2.1.1.3

Raising $0$ to any positive power yields $0$ .

$8 = 6859 a + b \cdot 0 + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.12.2.1.1.4

Multiply $b$ by $0$ .

$8 = 6859 a + 0 + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$8 = 6859 a + 0 + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.12.2.1.2

Add $6859 a$ and $0$ .

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + d$

Step 3.3.2.13

Replace all occurrences of $d$ in $6 = a \cdot 22^{3} + b \cdot 0^{2} + d$ with $9$ .

$6 = a \cdot 22^{3} + b \cdot 0^{2} + 9$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.2.14

Simplify $6 = a \cdot 22^{3} + b \cdot 0^{2} + 9$ .

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Step 3.3.2.14.1

Simplify the left side.

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Step 3.3.2.14.1.1

Remove parentheses.

$6 = a \cdot 22^{3} + b \cdot 0^{2} + 9$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = a \cdot 22^{3} + b \cdot 0^{2} + 9$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.2.14.2

Simplify the right side.

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Step 3.3.2.14.2.1

Simplify $a \cdot 22^{3} + b \cdot 0^{2} + 9$ .

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Step 3.3.2.14.2.1.1

Simplify each term.

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Step 3.3.2.14.2.1.1.1

Raise $22$ to the power of $3$ .

$6 = a \cdot 10648 + b \cdot 0^{2} + 9$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.2.14.2.1.1.2

Move $10648$ to the left of $a$ .

$6 = 10648 \cdot a + b \cdot 0^{2} + 9$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.2.14.2.1.1.3

Raising $0$ to any positive power yields $0$ .

$6 = 10648 a + b \cdot 0 + 9$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.2.14.2.1.1.4

Multiply $b$ by $0$ .

$6 = 10648 a + 0 + 9$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = 10648 a + 0 + 9$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.2.14.2.1.2

Add $10648 a$ and $0$ .

$6 = 10648 a + 9$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = 10648 a + 9$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = 10648 a + 9$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = 10648 a + 9$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = 10648 a + 9$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.3

Solve for $a$ in $6 = 10648 a + 9$ .

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Step 3.3.3.1

Rewrite the equation as $10648 a + 9 = 6$ .

$10648 a + 9 = 6$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.3.2

Move all terms not containing $a$ to the right side of the equation.

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Step 3.3.3.2.1

Subtract $9$ from both sides of the equation.

$10648 a = 6 - 9$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.3.2.2

Subtract $9$ from $6$ .

$10648 a = - 3$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$10648 a = - 3$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.3.3

Divide each term in $10648 a = - 3$ by $10648$ and simplify.

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Step 3.3.3.3.1

Divide each term in $10648 a = - 3$ by $10648$ .

$\frac{10648 a}{10648} = \frac{- 3}{10648}$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.3.3.2

Simplify the left side.

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Step 3.3.3.3.2.1

Cancel the common factor of $10648$ .

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Step 3.3.3.3.2.1.1

Cancel the common factor.

$\frac{10648 a}{10648} = \frac{- 3}{10648}$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.3.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 3}{10648}$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$a = \frac{- 3}{10648}$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$a = \frac{- 3}{10648}$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.3.3.3

Simplify the right side.

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Step 3.3.3.3.3.1

Move the negative in front of the fraction.

$a = - \frac{3}{10648}$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$a = - \frac{3}{10648}$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$a = - \frac{3}{10648}$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$a = - \frac{3}{10648}$

$8 = 6859 a + 9$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4

Replace all occurrences of $a$ with $- \frac{3}{10648}$ in each equation.

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Step 3.3.4.1

Replace all occurrences of $a$ in $8 = 6859 a + 9$ with $- \frac{3}{10648}$ .

$8 = 6859 (- \frac{3}{10648}) + 9$

$a = - \frac{3}{10648}$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.2

Simplify the right side.

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Step 3.3.4.2.1

Simplify $6859 (- \frac{3}{10648}) + 9$ .

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Step 3.3.4.2.1.1

Simplify each term.

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Step 3.3.4.2.1.1.1

Multiply $6859 (- \frac{3}{10648})$ .

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Step 3.3.4.2.1.1.1.1

Multiply $- 1$ by $6859$ .

$8 = - 6859 (\frac{3}{10648}) + 9$

$a = - \frac{3}{10648}$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.2.1.1.1.2

Combine $- 6859$ and $\frac{3}{10648}$ .

$8 = \frac{- 6859 \cdot 3}{10648} + 9$

$a = - \frac{3}{10648}$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.2.1.1.1.3

Multiply $- 6859$ by $3$ .

$8 = \frac{- 20577}{10648} + 9$

$a = - \frac{3}{10648}$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$8 = \frac{- 20577}{10648} + 9$

$a = - \frac{3}{10648}$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.2.1.1.2

Move the negative in front of the fraction.

$8 = - \frac{20577}{10648} + 9$

$a = - \frac{3}{10648}$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$8 = - \frac{20577}{10648} + 9$

$a = - \frac{3}{10648}$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.2.1.2

To write $9$ as a fraction with a common denominator, multiply by $\frac{10648}{10648}$ .

$8 = - \frac{20577}{10648} + 9 \cdot \frac{10648}{10648}$

$a = - \frac{3}{10648}$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.2.1.3

Combine $9$ and $\frac{10648}{10648}$ .

$8 = - \frac{20577}{10648} + \frac{9 \cdot 10648}{10648}$

$a = - \frac{3}{10648}$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.2.1.4

Combine the numerators over the common denominator.

$8 = \frac{- 20577 + 9 \cdot 10648}{10648}$

$a = - \frac{3}{10648}$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.2.1.5

Simplify the numerator.

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Step 3.3.4.2.1.5.1

Multiply $9$ by $10648$ .

$8 = \frac{- 20577 + 95832}{10648}$

$a = - \frac{3}{10648}$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.2.1.5.2

Add $- 20577$ and $95832$ .

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 4096 a + 9$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.3

Replace all occurrences of $a$ in $7 = 4096 a + 9$ with $- \frac{3}{10648}$ .

$7 = 4096 (- \frac{3}{10648}) + 9$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.4

Simplify the right side.

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Step 3.3.4.4.1

Simplify $4096 (- \frac{3}{10648}) + 9$ .

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Step 3.3.4.4.1.1

Simplify each term.

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Step 3.3.4.4.1.1.1

Cancel the common factor of $8$ .

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Step 3.3.4.4.1.1.1.1

Move the leading negative in $- \frac{3}{10648}$ into the numerator.

$7 = 4096 (\frac{- 3}{10648}) + 9$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.4.1.1.1.2

Factor $8$ out of $4096$ .

$7 = 8 (512) (\frac{- 3}{10648}) + 9$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.4.1.1.1.3

Factor $8$ out of $10648$ .

$7 = 8 \cdot (512 (\frac{- 3}{8 \cdot 1331})) + 9$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.4.1.1.1.4

Cancel the common factor.

$7 = 8 \cdot (512 (\frac{- 3}{8 \cdot 1331})) + 9$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.4.1.1.1.5

Rewrite the expression.

$7 = 512 (\frac{- 3}{1331}) + 9$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$7 = 512 (\frac{- 3}{1331}) + 9$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.4.1.1.2

Combine $512$ and $\frac{- 3}{1331}$ .

$7 = \frac{512 \cdot - 3}{1331} + 9$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.4.1.1.3

Multiply $512$ by $- 3$ .

$7 = \frac{- 1536}{1331} + 9$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.4.1.1.4

Move the negative in front of the fraction.

$7 = - \frac{1536}{1331} + 9$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$7 = - \frac{1536}{1331} + 9$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.4.1.2

To write $9$ as a fraction with a common denominator, multiply by $\frac{1331}{1331}$ .

$7 = - \frac{1536}{1331} + 9 \cdot \frac{1331}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.4.1.3

Combine $9$ and $\frac{1331}{1331}$ .

$7 = - \frac{1536}{1331} + \frac{9 \cdot 1331}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.4.1.4

Combine the numerators over the common denominator.

$7 = \frac{- 1536 + 9 \cdot 1331}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.4.1.5

Simplify the numerator.

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Step 3.3.4.4.1.5.1

Multiply $9$ by $1331$ .

$7 = \frac{- 1536 + 11979}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.4.1.5.2

Add $- 1536$ and $11979$ .

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$9 = 2197 a + 9$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.5

Replace all occurrences of $a$ in $9 = 2197 a + 9$ with $- \frac{3}{10648}$ .

$9 = 2197 (- \frac{3}{10648}) + 9$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.6

Simplify the right side.

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Step 3.3.4.6.1

Simplify $2197 (- \frac{3}{10648}) + 9$ .

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Step 3.3.4.6.1.1

Simplify each term.

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Step 3.3.4.6.1.1.1

Multiply $2197 (- \frac{3}{10648})$ .

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Step 3.3.4.6.1.1.1.1

Multiply $- 1$ by $2197$ .

$9 = - 2197 (\frac{3}{10648}) + 9$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.6.1.1.1.2

Combine $- 2197$ and $\frac{3}{10648}$ .

$9 = \frac{- 2197 \cdot 3}{10648} + 9$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.6.1.1.1.3

Multiply $- 2197$ by $3$ .

$9 = \frac{- 6591}{10648} + 9$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$9 = \frac{- 6591}{10648} + 9$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.6.1.1.2

Move the negative in front of the fraction.

$9 = - \frac{6591}{10648} + 9$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$9 = - \frac{6591}{10648} + 9$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.6.1.2

To write $9$ as a fraction with a common denominator, multiply by $\frac{10648}{10648}$ .

$9 = - \frac{6591}{10648} + 9 \cdot \frac{10648}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.6.1.3

Combine $9$ and $\frac{10648}{10648}$ .

$9 = - \frac{6591}{10648} + \frac{9 \cdot 10648}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.6.1.4

Combine the numerators over the common denominator.

$9 = \frac{- 6591 + 9 \cdot 10648}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.6.1.5

Simplify the numerator.

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Step 3.3.4.6.1.5.1

Multiply $9$ by $10648$ .

$9 = \frac{- 6591 + 95832}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.6.1.5.2

Add $- 6591$ and $95832$ .

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$6 = 729 a + 9$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.7

Replace all occurrences of $a$ in $6 = 729 a + 9$ with $- \frac{3}{10648}$ .

$6 = 729 (- \frac{3}{10648}) + 9$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.8

Simplify the right side.

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Step 3.3.4.8.1

Simplify $729 (- \frac{3}{10648}) + 9$ .

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Step 3.3.4.8.1.1

Simplify each term.

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Step 3.3.4.8.1.1.1

Multiply $729 (- \frac{3}{10648})$ .

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Step 3.3.4.8.1.1.1.1

Multiply $- 1$ by $729$ .

$6 = - 729 (\frac{3}{10648}) + 9$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.8.1.1.1.2

Combine $- 729$ and $\frac{3}{10648}$ .

$6 = \frac{- 729 \cdot 3}{10648} + 9$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.8.1.1.1.3

Multiply $- 729$ by $3$ .

$6 = \frac{- 2187}{10648} + 9$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = \frac{- 2187}{10648} + 9$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.8.1.1.2

Move the negative in front of the fraction.

$6 = - \frac{2187}{10648} + 9$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = - \frac{2187}{10648} + 9$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.8.1.2

To write $9$ as a fraction with a common denominator, multiply by $\frac{10648}{10648}$ .

$6 = - \frac{2187}{10648} + 9 \cdot \frac{10648}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.8.1.3

Combine $9$ and $\frac{10648}{10648}$ .

$6 = - \frac{2187}{10648} + \frac{9 \cdot 10648}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.8.1.4

Combine the numerators over the common denominator.

$6 = \frac{- 2187 + 9 \cdot 10648}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.8.1.5

Simplify the numerator.

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Step 3.3.4.8.1.5.1

Multiply $9$ by $10648$ .

$6 = \frac{- 2187 + 95832}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.8.1.5.2

Add $- 2187$ and $95832$ .

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 216 a + 9$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.9

Replace all occurrences of $a$ in $7 = 216 a + 9$ with $- \frac{3}{10648}$ .

$7 = 216 (- \frac{3}{10648}) + 9$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.10

Simplify the right side.

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Step 3.3.4.10.1

Simplify $216 (- \frac{3}{10648}) + 9$ .

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Step 3.3.4.10.1.1

Simplify each term.

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Step 3.3.4.10.1.1.1

Cancel the common factor of $8$ .

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Step 3.3.4.10.1.1.1.1

Move the leading negative in $- \frac{3}{10648}$ into the numerator.

$7 = 216 (\frac{- 3}{10648}) + 9$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.10.1.1.1.2

Factor $8$ out of $216$ .

$7 = 8 (27) (\frac{- 3}{10648}) + 9$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.10.1.1.1.3

Factor $8$ out of $10648$ .

$7 = 8 \cdot (27 (\frac{- 3}{8 \cdot 1331})) + 9$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.10.1.1.1.4

Cancel the common factor.

$7 = 8 \cdot (27 (\frac{- 3}{8 \cdot 1331})) + 9$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.10.1.1.1.5

Rewrite the expression.

$7 = 27 (\frac{- 3}{1331}) + 9$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 125 a + 9$

$d = 9$

$7 = 27 (\frac{- 3}{1331}) + 9$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.10.1.1.2

Combine $27$ and $\frac{- 3}{1331}$ .

$7 = \frac{27 \cdot - 3}{1331} + 9$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.10.1.1.3

Multiply $27$ by $- 3$ .

$7 = \frac{- 81}{1331} + 9$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.10.1.1.4

Move the negative in front of the fraction.

$7 = - \frac{81}{1331} + 9$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 125 a + 9$

$d = 9$

$7 = - \frac{81}{1331} + 9$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.10.1.2

To write $9$ as a fraction with a common denominator, multiply by $\frac{1331}{1331}$ .

$7 = - \frac{81}{1331} + 9 \cdot \frac{1331}{1331}$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.10.1.3

Combine $9$ and $\frac{1331}{1331}$ .

$7 = - \frac{81}{1331} + \frac{9 \cdot 1331}{1331}$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.10.1.4

Combine the numerators over the common denominator.

$7 = \frac{- 81 + 9 \cdot 1331}{1331}$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.10.1.5

Simplify the numerator.

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Step 3.3.4.10.1.5.1

Multiply $9$ by $1331$ .

$7 = \frac{- 81 + 11979}{1331}$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.10.1.5.2

Add $- 81$ and $11979$ .

$7 = \frac{11898}{1331}$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 125 a + 9$

$d = 9$

$7 = \frac{11898}{1331}$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 125 a + 9$

$d = 9$

$7 = \frac{11898}{1331}$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 125 a + 9$

$d = 9$

$7 = \frac{11898}{1331}$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$7 = 125 a + 9$

$d = 9$

Step 3.3.4.11

Replace all occurrences of $a$ in $7 = 125 a + 9$ with $- \frac{3}{10648}$ .

$7 = 125 (- \frac{3}{10648}) + 9$

$7 = \frac{11898}{1331}$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$d = 9$

Step 3.3.4.12

Simplify the right side.

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Step 3.3.4.12.1

Simplify $125 (- \frac{3}{10648}) + 9$ .

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Step 3.3.4.12.1.1

Simplify each term.

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Step 3.3.4.12.1.1.1

Multiply $125 (- \frac{3}{10648})$ .

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Step 3.3.4.12.1.1.1.1

Multiply $- 1$ by $125$ .

$7 = - 125 (\frac{3}{10648}) + 9$

$7 = \frac{11898}{1331}$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$d = 9$

Step 3.3.4.12.1.1.1.2

Combine $- 125$ and $\frac{3}{10648}$ .

$7 = \frac{- 125 \cdot 3}{10648} + 9$

$7 = \frac{11898}{1331}$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$d = 9$

Step 3.3.4.12.1.1.1.3

Multiply $- 125$ by $3$ .

$7 = \frac{- 375}{10648} + 9$

$7 = \frac{11898}{1331}$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$d = 9$

$7 = \frac{- 375}{10648} + 9$

$7 = \frac{11898}{1331}$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$d = 9$

Step 3.3.4.12.1.1.2

Move the negative in front of the fraction.

$7 = - \frac{375}{10648} + 9$

$7 = \frac{11898}{1331}$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$d = 9$

$7 = - \frac{375}{10648} + 9$

$7 = \frac{11898}{1331}$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$d = 9$

Step 3.3.4.12.1.2

To write $9$ as a fraction with a common denominator, multiply by $\frac{10648}{10648}$ .

$7 = - \frac{375}{10648} + 9 \cdot \frac{10648}{10648}$

$7 = \frac{11898}{1331}$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$d = 9$

Step 3.3.4.12.1.3

Combine $9$ and $\frac{10648}{10648}$ .

$7 = - \frac{375}{10648} + \frac{9 \cdot 10648}{10648}$

$7 = \frac{11898}{1331}$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$d = 9$

Step 3.3.4.12.1.4

Combine the numerators over the common denominator.

$7 = \frac{- 375 + 9 \cdot 10648}{10648}$

$7 = \frac{11898}{1331}$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$d = 9$

Step 3.3.4.12.1.5

Simplify the numerator.

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Step 3.3.4.12.1.5.1

Multiply $9$ by $10648$ .

$7 = \frac{- 375 + 95832}{10648}$

$7 = \frac{11898}{1331}$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$d = 9$

Step 3.3.4.12.1.5.2

Add $- 375$ and $95832$ .

$7 = \frac{95457}{10648}$

$7 = \frac{11898}{1331}$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$d = 9$

$7 = \frac{95457}{10648}$

$7 = \frac{11898}{1331}$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$d = 9$

$7 = \frac{95457}{10648}$

$7 = \frac{11898}{1331}$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$d = 9$

$7 = \frac{95457}{10648}$

$7 = \frac{11898}{1331}$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$d = 9$

$7 = \frac{95457}{10648}$

$7 = \frac{11898}{1331}$

$6 = \frac{93645}{10648}$

$9 = \frac{89241}{10648}$

$7 = \frac{10443}{1331}$

$8 = \frac{75255}{10648}$

$a = - \frac{3}{10648}$

$d = 9$

Step 3.3.5

Since $7 = \frac{95457}{10648}$ is not true, there is no solution.

No solution

Step 3.4

Calculate the value of $y$ using each $x$ value in the table and compare this value to the given $y$ value in the table.

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Step 3.4.1

Calculate the value of $y$ such that $y = a x^{3} + b$ when $a = 0$ , $b = 0$ , $c = 0$ , $d = 0$ , and $x = 0$ .

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Step 3.4.1.1

Simplify each term.

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Step 3.4.1.1.1

Multiply $0$ by ${(0)}^{3}$ by adding the exponents.

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Step 3.4.1.1.1.1

Multiply $0$ by ${(0)}^{3}$ .

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Step 3.4.1.1.1.1.1

Raise $0$ to the power of $1$ .

$y = 0 \cdot {(0)}^{3} + (0) \cdot (0^{2}) + (0) \cdot ((0) \cdot 0)$

Step 3.4.1.1.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = 0^{1 + 3} + (0) \cdot (0^{2}) + (0) \cdot ((0) \cdot 0)$

Step 3.4.1.1.1.2

Add $1$ and $3$ .

$y = 0^{4} + (0) \cdot (0^{2}) + (0) \cdot ((0) \cdot 0)$

Step 3.4.1.1.2

Raising $0$ to any positive power yields $0$ .

$y = 0 + (0) \cdot (0^{2}) + (0) \cdot ((0) \cdot 0)$

Step 3.4.1.1.3

Multiply $0$ by $0^{2}$ by adding the exponents.

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Step 3.4.1.1.3.1

Multiply $0$ by $0^{2}$ .

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Step 3.4.1.1.3.1.1

Raise $0$ to the power of $1$ .

$y = 0 + 0 \cdot 0^{2} + (0) \cdot ((0) \cdot 0)$

Step 3.4.1.1.3.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = 0 + 0^{1 + 2} + (0) \cdot ((0) \cdot 0)$

Step 3.4.1.1.3.2

Add $1$ and $2$ .

$y = 0 + 0^{3} + (0) \cdot ((0) \cdot 0)$

Step 3.4.1.1.4

Raising $0$ to any positive power yields $0$ .

$y = 0 + 0 + (0) \cdot ((0) \cdot 0)$

Step 3.4.1.1.5

Multiply $(0) ((0) \cdot 0)$ .

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Step 3.4.1.1.5.1

Multiply $0$ by $0$ .

$y = 0 + 0 + 0 \cdot 0$

Step 3.4.1.1.5.2

Multiply $0$ by $0$ .

$y = 0 + 0 + 0$

Step 3.4.1.2

Simplify by adding numbers.

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Step 3.4.1.2.1

Add $0$ and $0$ .

$y = 0 + 0$

Step 3.4.1.2.2

Add $0$ and $0$ .

$y = 0$

Step 3.4.2

If the table has a cubic function rule, $y = y$ for the corresponding $x$ value, $x = 0$ . This check does not pass, since $y = 0$ and $y = 9$ . The function rule can't be cubic.

$0 \neq 9$

Step 3.4.3

Since $y \neq y$ for the corresponding $x$ values, the function is not cubic.

The function is not cubic

Step 4

There are no values for $a$ , $b$ , $c$ , and $d$ in the equations $y = a x + b$ , $y = a x^{2} + b x + c$ , and $y = a x^{3} + b x^{2} + c x + d$ that work for every pair of $x$ and $y$ .

The table does not have a function rule that is linear, quadratic, or cubic.