Pre-Algebra Examples

$\begin{array}{c} x & y \\ 1 & 8.7 \\ 2 & 8.7 \\ 3 & 9.2 \\ 4 & 9.5 \\ 5 & 9.9 \\ 6 & 9.9 \\ 7 & 10.1 \end{array}$

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 $y = a x + b$ .

$8.7 = a (1) + b 8.7 = a (2) + b 9.2 = a (3) + b 9.5 = a (4) + b 9.9 = a (5) + b 9.9 = a (6) + b 10.1 = a (7) + b$

Step 1.3

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

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Step 1.3.1

Solve for $a$ in $8.7 = a + b$ .

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Step 1.3.1.1

Rewrite the equation as $a + b = 8.7$ .

$a + b = 8.7$

$8.7 = a (2) + b$

$9.2 = a (3) + b$

$9.5 = a (4) + b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

Step 1.3.1.2

Subtract $b$ from both sides of the equation.

$a = 8.7 - b$

$8.7 = a (2) + b$

$9.2 = a (3) + b$

$9.5 = a (4) + b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

$a = 8.7 - b$

$8.7 = a (2) + b$

$9.2 = a (3) + b$

$9.5 = a (4) + b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

Step 1.3.2

Replace all occurrences of $a$ with $8.7 - b$ in each equation.

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Step 1.3.2.1

Replace all occurrences of $a$ in $8.7 = a (2) + b$ with $8.7 - b$ .

$8.7 = (8.7 - b) (2) + b$

$a = 8.7 - b$

$9.2 = a (3) + b$

$9.5 = a (4) + b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

Step 1.3.2.2

Simplify the right side.

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Step 1.3.2.2.1

Simplify $(8.7 - b) (2) + b$ .

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Step 1.3.2.2.1.1

Simplify each term.

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Step 1.3.2.2.1.1.1

Apply the distributive property.

$8.7 = 8.7 \cdot 2 - b \cdot 2 + b$

$a = 8.7 - b$

$9.2 = a (3) + b$

$9.5 = a (4) + b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

Step 1.3.2.2.1.1.2

Multiply $8.7$ by $2$ .

$8.7 = 17.4 - b \cdot 2 + b$

$a = 8.7 - b$

$9.2 = a (3) + b$

$9.5 = a (4) + b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

Step 1.3.2.2.1.1.3

Multiply $2$ by $- 1$ .

$8.7 = 17.4 - 2 b + b$

$a = 8.7 - b$

$9.2 = a (3) + b$

$9.5 = a (4) + b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

$8.7 = 17.4 - 2 b + b$

$a = 8.7 - b$

$9.2 = a (3) + b$

$9.5 = a (4) + b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

Step 1.3.2.2.1.2

Add $- 2 b$ and $b$ .

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.2 = a (3) + b$

$9.5 = a (4) + b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.2 = a (3) + b$

$9.5 = a (4) + b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.2 = a (3) + b$

$9.5 = a (4) + b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

Step 1.3.2.3

Replace all occurrences of $a$ in $9.2 = a (3) + b$ with $8.7 - b$ .

$9.2 = (8.7 - b) (3) + b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.5 = a (4) + b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

Step 1.3.2.4

Simplify the right side.

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Step 1.3.2.4.1

Simplify $(8.7 - b) (3) + b$ .

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Step 1.3.2.4.1.1

Simplify each term.

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Step 1.3.2.4.1.1.1

Apply the distributive property.

$9.2 = 8.7 \cdot 3 - b \cdot 3 + b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.5 = a (4) + b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

Step 1.3.2.4.1.1.2

Multiply $8.7$ by $3$ .

$9.2 = 26.1 - b \cdot 3 + b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.5 = a (4) + b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

Step 1.3.2.4.1.1.3

Multiply $3$ by $- 1$ .

$9.2 = 26.1 - 3 b + b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.5 = a (4) + b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

$9.2 = 26.1 - 3 b + b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.5 = a (4) + b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

Step 1.3.2.4.1.2

Add $- 3 b$ and $b$ .

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.5 = a (4) + b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.5 = a (4) + b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.5 = a (4) + b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

Step 1.3.2.5

Replace all occurrences of $a$ in $9.5 = a (4) + b$ with $8.7 - b$ .

$9.5 = (8.7 - b) (4) + b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

Step 1.3.2.6

Simplify the right side.

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Step 1.3.2.6.1

Simplify $(8.7 - b) (4) + b$ .

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Step 1.3.2.6.1.1

Simplify each term.

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Step 1.3.2.6.1.1.1

Apply the distributive property.

$9.5 = 8.7 \cdot 4 - b \cdot 4 + b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

Step 1.3.2.6.1.1.2

Multiply $8.7$ by $4$ .

$9.5 = 34.8 - b \cdot 4 + b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

Step 1.3.2.6.1.1.3

Multiply $4$ by $- 1$ .

$9.5 = 34.8 - 4 b + b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

$9.5 = 34.8 - 4 b + b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

Step 1.3.2.6.1.2

Add $- 4 b$ and $b$ .

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.9 = a (5) + b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

Step 1.3.2.7

Replace all occurrences of $a$ in $9.9 = a (5) + b$ with $8.7 - b$ .

$9.9 = (8.7 - b) (5) + b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

Step 1.3.2.8

Simplify the right side.

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Step 1.3.2.8.1

Simplify $(8.7 - b) (5) + b$ .

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Step 1.3.2.8.1.1

Simplify each term.

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Step 1.3.2.8.1.1.1

Apply the distributive property.

$9.9 = 8.7 \cdot 5 - b \cdot 5 + b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

Step 1.3.2.8.1.1.2

Multiply $8.7$ by $5$ .

$9.9 = 43.5 - b \cdot 5 + b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

Step 1.3.2.8.1.1.3

Multiply $5$ by $- 1$ .

$9.9 = 43.5 - 5 b + b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

$9.9 = 43.5 - 5 b + b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

Step 1.3.2.8.1.2

Add $- 5 b$ and $b$ .

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.9 = a (6) + b$

$10.1 = a (7) + b$

Step 1.3.2.9

Replace all occurrences of $a$ in $9.9 = a (6) + b$ with $8.7 - b$ .

$9.9 = (8.7 - b) (6) + b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$10.1 = a (7) + b$

Step 1.3.2.10

Simplify the right side.

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Step 1.3.2.10.1

Simplify $(8.7 - b) (6) + b$ .

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Step 1.3.2.10.1.1

Simplify each term.

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Step 1.3.2.10.1.1.1

Apply the distributive property.

$9.9 = 8.7 \cdot 6 - b \cdot 6 + b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$10.1 = a (7) + b$

Step 1.3.2.10.1.1.2

Multiply $8.7$ by $6$ .

$9.9 = 52.2 - b \cdot 6 + b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$10.1 = a (7) + b$

Step 1.3.2.10.1.1.3

Multiply $6$ by $- 1$ .

$9.9 = 52.2 - 6 b + b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$10.1 = a (7) + b$

$9.9 = 52.2 - 6 b + b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$10.1 = a (7) + b$

Step 1.3.2.10.1.2

Add $- 6 b$ and $b$ .

$9.9 = 52.2 - 5 b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$10.1 = a (7) + b$

$9.9 = 52.2 - 5 b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$10.1 = a (7) + b$

$9.9 = 52.2 - 5 b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$10.1 = a (7) + b$

Step 1.3.2.11

Replace all occurrences of $a$ in $10.1 = a (7) + b$ with $8.7 - b$ .

$10.1 = (8.7 - b) (7) + b$

$9.9 = 52.2 - 5 b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

Step 1.3.2.12

Simplify the right side.

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Step 1.3.2.12.1

Simplify $(8.7 - b) (7) + b$ .

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Step 1.3.2.12.1.1

Simplify each term.

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Step 1.3.2.12.1.1.1

Apply the distributive property.

$10.1 = 8.7 \cdot 7 - b \cdot 7 + b$

$9.9 = 52.2 - 5 b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

Step 1.3.2.12.1.1.2

Multiply $8.7$ by $7$ .

$10.1 = 60.9 - b \cdot 7 + b$

$9.9 = 52.2 - 5 b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

Step 1.3.2.12.1.1.3

Multiply $7$ by $- 1$ .

$10.1 = 60.9 - 7 b + b$

$9.9 = 52.2 - 5 b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$10.1 = 60.9 - 7 b + b$

$9.9 = 52.2 - 5 b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

Step 1.3.2.12.1.2

Add $- 7 b$ and $b$ .

$10.1 = 60.9 - 6 b$

$9.9 = 52.2 - 5 b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$10.1 = 60.9 - 6 b$

$9.9 = 52.2 - 5 b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$10.1 = 60.9 - 6 b$

$9.9 = 52.2 - 5 b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$10.1 = 60.9 - 6 b$

$9.9 = 52.2 - 5 b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

Step 1.3.3

Solve for $b$ in $10.1 = 60.9 - 6 b$ .

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Step 1.3.3.1

Rewrite the equation as $60.9 - 6 b = 10.1$ .

$60.9 - 6 b = 10.1$

$9.9 = 52.2 - 5 b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

Step 1.3.3.2

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

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Step 1.3.3.2.1

Subtract $60.9$ from both sides of the equation.

$- 6 b = 10.1 - 60.9$

$9.9 = 52.2 - 5 b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

Step 1.3.3.2.2

Subtract $60.9$ from $10.1$ .

$- 6 b = - 50.8$

$9.9 = 52.2 - 5 b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$- 6 b = - 50.8$

$9.9 = 52.2 - 5 b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

Step 1.3.3.3

Divide each term in $- 6 b = - 50.8$ by $- 6$ and simplify.

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Step 1.3.3.3.1

Divide each term in $- 6 b = - 50.8$ by $- 6$ .

$\frac{- 6 b}{- 6} = \frac{- 50.8}{- 6}$

$9.9 = 52.2 - 5 b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

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 $- 6$ .

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Step 1.3.3.3.2.1.1

Cancel the common factor.

$\frac{- 6 b}{- 6} = \frac{- 50.8}{- 6}$

$9.9 = 52.2 - 5 b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

Step 1.3.3.3.2.1.2

Divide $b$ by $1$ .

$b = \frac{- 50.8}{- 6}$

$9.9 = 52.2 - 5 b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$b = \frac{- 50.8}{- 6}$

$9.9 = 52.2 - 5 b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$b = \frac{- 50.8}{- 6}$

$9.9 = 52.2 - 5 b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

Step 1.3.3.3.3

Simplify the right side.

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Step 1.3.3.3.3.1

Divide $- 50.8$ by $- 6$ .

$b = 8.4\overline{6}$

$9.9 = 52.2 - 5 b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$b = 8.4\overline{6}$

$9.9 = 52.2 - 5 b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$b = 8.4\overline{6}$

$9.9 = 52.2 - 5 b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$b = 8.4\overline{6}$

$9.9 = 52.2 - 5 b$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

Step 1.3.4

Replace all occurrences of $b$ with $8.4\overline{6}$ in each equation.

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Step 1.3.4.1

Replace all occurrences of $b$ in $9.9 = 52.2 - 5 b$ with $8.4\overline{6}$ .

$9.9 = 52.2 - 5 \cdot 8.4\overline{6}$

$b = 8.4\overline{6}$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

Step 1.3.4.2

Simplify the right side.

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Step 1.3.4.2.1

Simplify $52.2 - 5 \cdot 8.4\overline{6}$ .

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Step 1.3.4.2.1.1

Multiply $- 5$ by $8.4\overline{6}$ .

$9.9 = 52.2 - 42.\overline{3}$

$b = 8.4\overline{6}$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

Step 1.3.4.2.1.2

Subtract $42.\overline{3}$ from $52.2$ .

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

$9.9 = 43.5 - 4 b$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

Step 1.3.4.3

Replace all occurrences of $b$ in $9.9 = 43.5 - 4 b$ with $8.4\overline{6}$ .

$9.9 = 43.5 - 4 \cdot 8.4\overline{6}$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

Step 1.3.4.4

Simplify the right side.

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Step 1.3.4.4.1

Simplify $43.5 - 4 \cdot 8.4\overline{6}$ .

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Step 1.3.4.4.1.1

Multiply $- 4$ by $8.4\overline{6}$ .

$9.9 = 43.5 - 33.8\overline{6}$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

Step 1.3.4.4.1.2

Subtract $33.8\overline{6}$ from $43.5$ .

$9.9 = 9.6\overline{3}$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.9 = 9.6\overline{3}$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.9 = 9.6\overline{3}$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

$9.5 = 34.8 - 3 b$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

Step 1.3.4.5

Replace all occurrences of $b$ in $9.5 = 34.8 - 3 b$ with $8.4\overline{6}$ .

$9.5 = 34.8 - 3 \cdot 8.4\overline{6}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

Step 1.3.4.6

Simplify the right side.

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Step 1.3.4.6.1

Simplify $34.8 - 3 \cdot 8.4\overline{6}$ .

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Step 1.3.4.6.1.1

Multiply $- 3$ by $8.4\overline{6}$ .

$9.5 = 34.8 - 25.4$

$9.9 = 9.6\overline{3}$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

Step 1.3.4.6.1.2

Subtract $25.4$ from $34.8$ .

$9.5 = 9.3\overline{9}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.5 = 9.3\overline{9}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.5 = 9.3\overline{9}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

$9.2 = 26.1 - 2 b$

$8.7 = 17.4 - b$

$a = 8.7 - b$

Step 1.3.4.7

Replace all occurrences of $b$ in $9.2 = 26.1 - 2 b$ with $8.4\overline{6}$ .

$9.2 = 26.1 - 2 \cdot 8.4\overline{6}$

$9.5 = 9.3\overline{9}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

$8.7 = 17.4 - b$

$a = 8.7 - b$

Step 1.3.4.8

Simplify the right side.

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Step 1.3.4.8.1

Simplify $26.1 - 2 \cdot 8.4\overline{6}$ .

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Step 1.3.4.8.1.1

Multiply $- 2$ by $8.4\overline{6}$ .

$9.2 = 26.1 - 16.9\overline{3}$

$9.5 = 9.3\overline{9}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

$8.7 = 17.4 - b$

$a = 8.7 - b$

Step 1.3.4.8.1.2

Subtract $16.9\overline{3}$ from $26.1$ .

$9.2 = 9.1\overline{6}$

$9.5 = 9.3\overline{9}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.2 = 9.1\overline{6}$

$9.5 = 9.3\overline{9}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

$8.7 = 17.4 - b$

$a = 8.7 - b$

$9.2 = 9.1\overline{6}$

$9.5 = 9.3\overline{9}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

$8.7 = 17.4 - b$

$a = 8.7 - b$

Step 1.3.4.9

Replace all occurrences of $b$ in $8.7 = 17.4 - b$ with $8.4\overline{6}$ .

$8.7 = 17.4 - (8.4\overline{6})$

$9.2 = 9.1\overline{6}$

$9.5 = 9.3\overline{9}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

$a = 8.7 - b$

Step 1.3.4.10

Simplify the right side.

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Step 1.3.4.10.1

Simplify $17.4 - (8.4\overline{6})$ .

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Step 1.3.4.10.1.1

Multiply $- 1$ by $8.4\overline{6}$ .

$8.7 = 17.4 - 8.4\overline{6}$

$9.2 = 9.1\overline{6}$

$9.5 = 9.3\overline{9}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

$a = 8.7 - b$

Step 1.3.4.10.1.2

Subtract $8.4\overline{6}$ from $17.4$ .

$8.7 = 8.9\overline{3}$

$9.2 = 9.1\overline{6}$

$9.5 = 9.3\overline{9}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

$a = 8.7 - b$

$8.7 = 8.9\overline{3}$

$9.2 = 9.1\overline{6}$

$9.5 = 9.3\overline{9}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

$a = 8.7 - b$

$8.7 = 8.9\overline{3}$

$9.2 = 9.1\overline{6}$

$9.5 = 9.3\overline{9}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

$a = 8.7 - b$

Step 1.3.4.11

Replace all occurrences of $b$ in $a = 8.7 - b$ with $8.4\overline{6}$ .

$a = 8.7 - (8.4\overline{6})$

$8.7 = 8.9\overline{3}$

$9.2 = 9.1\overline{6}$

$9.5 = 9.3\overline{9}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

Step 1.3.4.12

Simplify the right side.

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Step 1.3.4.12.1

Simplify $8.7 - (8.4\overline{6})$ .

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Step 1.3.4.12.1.1

Multiply $- 1$ by $8.4\overline{6}$ .

$a = 8.7 - 8.4\overline{6}$

$8.7 = 8.9\overline{3}$

$9.2 = 9.1\overline{6}$

$9.5 = 9.3\overline{9}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

Step 1.3.4.12.1.2

Subtract $8.4\overline{6}$ from $8.7$ .

$a = 0.2\overline{3}$

$8.7 = 8.9\overline{3}$

$9.2 = 9.1\overline{6}$

$9.5 = 9.3\overline{9}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

$a = 0.2\overline{3}$

$8.7 = 8.9\overline{3}$

$9.2 = 9.1\overline{6}$

$9.5 = 9.3\overline{9}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

$a = 0.2\overline{3}$

$8.7 = 8.9\overline{3}$

$9.2 = 9.1\overline{6}$

$9.5 = 9.3\overline{9}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

$a = 0.2\overline{3}$

$8.7 = 8.9\overline{3}$

$9.2 = 9.1\overline{6}$

$9.5 = 9.3\overline{9}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.8\overline{6}$

$b = 8.4\overline{6}$

Step 1.3.5

Since $8.7 = 8.9\overline{3}$ 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 $a$ in $8.7 = a + b + c$ .

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Step 2.3.1.1

Rewrite the equation as $a + b + c = 8.7$ .

$a + b + c = 8.7$

$8.7 = a \cdot 2^{2} + b (2) + c$

$9.2 = a \cdot 3^{2} + b (3) + c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.1.2

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

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Step 2.3.1.2.1

Subtract $b$ from both sides of the equation.

$a + c = 8.7 - b$

$8.7 = a \cdot 2^{2} + b (2) + c$

$9.2 = a \cdot 3^{2} + b (3) + c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.1.2.2

Subtract $c$ from both sides of the equation.

$a = 8.7 - b - c$

$8.7 = a \cdot 2^{2} + b (2) + c$

$9.2 = a \cdot 3^{2} + b (3) + c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$a = 8.7 - b - c$

$8.7 = a \cdot 2^{2} + b (2) + c$

$9.2 = a \cdot 3^{2} + b (3) + c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$a = 8.7 - b - c$

$8.7 = a \cdot 2^{2} + b (2) + c$

$9.2 = a \cdot 3^{2} + b (3) + c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2

Replace all occurrences of $a$ with $8.7 - b - c$ in each equation.

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Step 2.3.2.1

Replace all occurrences of $a$ in $8.7 = a \cdot 2^{2} + b (2) + c$ with $8.7 - b - c$ .

$8.7 = (8.7 - b - c) \cdot 2^{2} + b (2) + c$

$a = 8.7 - b - c$

$9.2 = a \cdot 3^{2} + b (3) + c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.2

Simplify the right side.

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Step 2.3.2.2.1

Simplify $(8.7 - b - c) \cdot 2^{2} + b (2) + c$ .

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Step 2.3.2.2.1.1

Simplify each term.

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Step 2.3.2.2.1.1.1

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

$8.7 = (8.7 - b - c) \cdot 4 + b (2) + c$

$a = 8.7 - b - c$

$9.2 = a \cdot 3^{2} + b (3) + c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.2.1.1.2

Apply the distributive property.

$8.7 = 8.7 \cdot 4 - b \cdot 4 - c \cdot 4 + b (2) + c$

$a = 8.7 - b - c$

$9.2 = a \cdot 3^{2} + b (3) + c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.2.1.1.3

Simplify.

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Step 2.3.2.2.1.1.3.1

Multiply $8.7$ by $4$ .

$8.7 = 34.8 - b \cdot 4 - c \cdot 4 + b (2) + c$

$a = 8.7 - b - c$

$9.2 = a \cdot 3^{2} + b (3) + c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.2.1.1.3.2

Multiply $4$ by $- 1$ .

$8.7 = 34.8 - 4 b - c \cdot 4 + b (2) + c$

$a = 8.7 - b - c$

$9.2 = a \cdot 3^{2} + b (3) + c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.2.1.1.3.3

Multiply $4$ by $- 1$ .

$8.7 = 34.8 - 4 b - 4 c + b (2) + c$

$a = 8.7 - b - c$

$9.2 = a \cdot 3^{2} + b (3) + c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$8.7 = 34.8 - 4 b - 4 c + b (2) + c$

$a = 8.7 - b - c$

$9.2 = a \cdot 3^{2} + b (3) + c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.2.1.1.4

Move $2$ to the left of $b$ .

$8.7 = 34.8 - 4 b - 4 c + 2 b + c$

$a = 8.7 - b - c$

$9.2 = a \cdot 3^{2} + b (3) + c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$8.7 = 34.8 - 4 b - 4 c + 2 b + c$

$a = 8.7 - b - c$

$9.2 = a \cdot 3^{2} + b (3) + c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.2.1.2

Simplify by adding terms.

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Step 2.3.2.2.1.2.1

Add $- 4 b$ and $2 b$ .

$8.7 = 34.8 - 2 b - 4 c + c$

$a = 8.7 - b - c$

$9.2 = a \cdot 3^{2} + b (3) + c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.2.1.2.2

Add $- 4 c$ and $c$ .

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.2 = a \cdot 3^{2} + b (3) + c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.2 = a \cdot 3^{2} + b (3) + c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.2 = a \cdot 3^{2} + b (3) + c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.2 = a \cdot 3^{2} + b (3) + c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.3

Replace all occurrences of $a$ in $9.2 = a \cdot 3^{2} + b (3) + c$ with $8.7 - b - c$ .

$9.2 = (8.7 - b - c) \cdot 3^{2} + b (3) + c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.4

Simplify the right side.

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Step 2.3.2.4.1

Simplify $(8.7 - b - c) \cdot 3^{2} + b (3) + c$ .

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Step 2.3.2.4.1.1

Simplify each term.

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Step 2.3.2.4.1.1.1

Raise $3$ to the power of $2$ .

$9.2 = (8.7 - b - c) \cdot 9 + b (3) + c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.4.1.1.2

Apply the distributive property.

$9.2 = 8.7 \cdot 9 - b \cdot 9 - c \cdot 9 + b (3) + c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.4.1.1.3

Simplify.

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Step 2.3.2.4.1.1.3.1

Multiply $8.7$ by $9$ .

$9.2 = 78.3 - b \cdot 9 - c \cdot 9 + b (3) + c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.4.1.1.3.2

Multiply $9$ by $- 1$ .

$9.2 = 78.3 - 9 b - c \cdot 9 + b (3) + c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.4.1.1.3.3

Multiply $9$ by $- 1$ .

$9.2 = 78.3 - 9 b - 9 c + b (3) + c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$9.2 = 78.3 - 9 b - 9 c + b (3) + c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.4.1.1.4

Move $3$ to the left of $b$ .

$9.2 = 78.3 - 9 b - 9 c + 3 b + c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$9.2 = 78.3 - 9 b - 9 c + 3 b + c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.4.1.2

Simplify by adding terms.

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Step 2.3.2.4.1.2.1

Add $- 9 b$ and $3 b$ .

$9.2 = 78.3 - 6 b - 9 c + c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.4.1.2.2

Add $- 9 c$ and $c$ .

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.5 = a \cdot 4^{2} + b (4) + c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.5

Replace all occurrences of $a$ in $9.5 = a \cdot 4^{2} + b (4) + c$ with $8.7 - b - c$ .

$9.5 = (8.7 - b - c) \cdot 4^{2} + b (4) + c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.6

Simplify the right side.

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Step 2.3.2.6.1

Simplify $(8.7 - b - c) \cdot 4^{2} + b (4) + c$ .

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Step 2.3.2.6.1.1

Simplify each term.

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Step 2.3.2.6.1.1.1

Raise $4$ to the power of $2$ .

$9.5 = (8.7 - b - c) \cdot 16 + b (4) + c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.6.1.1.2

Apply the distributive property.

$9.5 = 8.7 \cdot 16 - b \cdot 16 - c \cdot 16 + b (4) + c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.6.1.1.3

Simplify.

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Step 2.3.2.6.1.1.3.1

Multiply $8.7$ by $16$ .

$9.5 = 139.2 - b \cdot 16 - c \cdot 16 + b (4) + c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.6.1.1.3.2

Multiply $16$ by $- 1$ .

$9.5 = 139.2 - 16 b - c \cdot 16 + b (4) + c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.6.1.1.3.3

Multiply $16$ by $- 1$ .

$9.5 = 139.2 - 16 b - 16 c + b (4) + c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$9.5 = 139.2 - 16 b - 16 c + b (4) + c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.6.1.1.4

Move $4$ to the left of $b$ .

$9.5 = 139.2 - 16 b - 16 c + 4 b + c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$9.5 = 139.2 - 16 b - 16 c + 4 b + c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.6.1.2

Simplify by adding terms.

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Step 2.3.2.6.1.2.1

Add $- 16 b$ and $4 b$ .

$9.5 = 139.2 - 12 b - 16 c + c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.6.1.2.2

Add $- 16 c$ and $c$ .

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 5^{2} + b (5) + c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.7

Replace all occurrences of $a$ in $9.9 = a \cdot 5^{2} + b (5) + c$ with $8.7 - b - c$ .

$9.9 = (8.7 - b - c) \cdot 5^{2} + b (5) + c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.8

Simplify the right side.

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Step 2.3.2.8.1

Simplify $(8.7 - b - c) \cdot 5^{2} + b (5) + c$ .

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Step 2.3.2.8.1.1

Simplify each term.

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Step 2.3.2.8.1.1.1

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

$9.9 = (8.7 - b - c) \cdot 25 + b (5) + c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.8.1.1.2

Apply the distributive property.

$9.9 = 8.7 \cdot 25 - b \cdot 25 - c \cdot 25 + b (5) + c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.8.1.1.3

Simplify.

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Step 2.3.2.8.1.1.3.1

Multiply $8.7$ by $25$ .

$9.9 = 217.5 - b \cdot 25 - c \cdot 25 + b (5) + c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.8.1.1.3.2

Multiply $25$ by $- 1$ .

$9.9 = 217.5 - 25 b - c \cdot 25 + b (5) + c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.8.1.1.3.3

Multiply $25$ by $- 1$ .

$9.9 = 217.5 - 25 b - 25 c + b (5) + c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$9.9 = 217.5 - 25 b - 25 c + b (5) + c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.8.1.1.4

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

$9.9 = 217.5 - 25 b - 25 c + 5 b + c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$9.9 = 217.5 - 25 b - 25 c + 5 b + c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.8.1.2

Simplify by adding terms.

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Step 2.3.2.8.1.2.1

Add $- 25 b$ and $5 b$ .

$9.9 = 217.5 - 20 b - 25 c + c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.8.1.2.2

Add $- 25 c$ and $c$ .

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = a \cdot 6^{2} + b (6) + c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.9

Replace all occurrences of $a$ in $9.9 = a \cdot 6^{2} + b (6) + c$ with $8.7 - b - c$ .

$9.9 = (8.7 - b - c) \cdot 6^{2} + b (6) + c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.10

Simplify the right side.

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Step 2.3.2.10.1

Simplify $(8.7 - b - c) \cdot 6^{2} + b (6) + c$ .

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Step 2.3.2.10.1.1

Simplify each term.

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Step 2.3.2.10.1.1.1

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

$9.9 = (8.7 - b - c) \cdot 36 + b (6) + c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.10.1.1.2

Apply the distributive property.

$9.9 = 8.7 \cdot 36 - b \cdot 36 - c \cdot 36 + b (6) + c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.10.1.1.3

Simplify.

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Step 2.3.2.10.1.1.3.1

Multiply $8.7$ by $36$ .

$9.9 = 313.2 - b \cdot 36 - c \cdot 36 + b (6) + c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.10.1.1.3.2

Multiply $36$ by $- 1$ .

$9.9 = 313.2 - 36 b - c \cdot 36 + b (6) + c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.10.1.1.3.3

Multiply $36$ by $- 1$ .

$9.9 = 313.2 - 36 b - 36 c + b (6) + c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$9.9 = 313.2 - 36 b - 36 c + b (6) + c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.10.1.1.4

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

$9.9 = 313.2 - 36 b - 36 c + 6 b + c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$9.9 = 313.2 - 36 b - 36 c + 6 b + c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.10.1.2

Simplify by adding terms.

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Step 2.3.2.10.1.2.1

Add $- 36 b$ and $6 b$ .

$9.9 = 313.2 - 30 b - 36 c + c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.10.1.2.2

Add $- 36 c$ and $c$ .

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$10.1 = a \cdot 7^{2} + b (7) + c$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$10.1 = a \cdot 7^{2} + b (7) + c$

Step 2.3.2.11

Replace all occurrences of $a$ in $10.1 = a \cdot 7^{2} + b (7) + c$ with $8.7 - b - c$ .

$10.1 = (8.7 - b - c) \cdot 7^{2} + b (7) + c$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.2.12

Simplify the right side.

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Step 2.3.2.12.1

Simplify $(8.7 - b - c) \cdot 7^{2} + b (7) + c$ .

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Step 2.3.2.12.1.1

Simplify each term.

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Step 2.3.2.12.1.1.1

Raise $7$ to the power of $2$ .

$10.1 = (8.7 - b - c) \cdot 49 + b (7) + c$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.2.12.1.1.2

Apply the distributive property.

$10.1 = 8.7 \cdot 49 - b \cdot 49 - c \cdot 49 + b (7) + c$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.2.12.1.1.3

Simplify.

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Step 2.3.2.12.1.1.3.1

Multiply $8.7$ by $49$ .

$10.1 = 426.3 - b \cdot 49 - c \cdot 49 + b (7) + c$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.2.12.1.1.3.2

Multiply $49$ by $- 1$ .

$10.1 = 426.3 - 49 b - c \cdot 49 + b (7) + c$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.2.12.1.1.3.3

Multiply $49$ by $- 1$ .

$10.1 = 426.3 - 49 b - 49 c + b (7) + c$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$10.1 = 426.3 - 49 b - 49 c + b (7) + c$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.2.12.1.1.4

Move $7$ to the left of $b$ .

$10.1 = 426.3 - 49 b - 49 c + 7 b + c$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$10.1 = 426.3 - 49 b - 49 c + 7 b + c$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.2.12.1.2

Simplify by adding terms.

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Step 2.3.2.12.1.2.1

Add $- 49 b$ and $7 b$ .

$10.1 = 426.3 - 42 b - 49 c + c$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.2.12.1.2.2

Add $- 49 c$ and $c$ .

$10.1 = 426.3 - 42 b - 48 c$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$10.1 = 426.3 - 42 b - 48 c$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$10.1 = 426.3 - 42 b - 48 c$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$10.1 = 426.3 - 42 b - 48 c$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$10.1 = 426.3 - 42 b - 48 c$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.3

Solve for $b$ in $10.1 = 426.3 - 42 b - 48 c$ .

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Step 2.3.3.1

Rewrite the equation as $426.3 - 42 b - 48 c = 10.1$ .

$426.3 - 42 b - 48 c = 10.1$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.3.2

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

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Step 2.3.3.2.1

Subtract $426.3$ from both sides of the equation.

$- 42 b - 48 c = 10.1 - 426.3$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.3.2.2

Add $48 c$ to both sides of the equation.

$- 42 b = 10.1 - 426.3 + 48 c$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.3.2.3

Subtract $426.3$ from $10.1$ .

$- 42 b = - 416.2 + 48 c$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$- 42 b = - 416.2 + 48 c$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.3.3

Divide each term in $- 42 b = - 416.2 + 48 c$ by $- 42$ and simplify.

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Step 2.3.3.3.1

Divide each term in $- 42 b = - 416.2 + 48 c$ by $- 42$ .

$\frac{- 42 b}{- 42} = \frac{- 416.2}{- 42} + \frac{48 c}{- 42}$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

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 $- 42$ .

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Step 2.3.3.3.2.1.1

Cancel the common factor.

$\frac{- 42 b}{- 42} = \frac{- 416.2}{- 42} + \frac{48 c}{- 42}$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.3.3.2.1.2

Divide $b$ by $1$ .

$b = \frac{- 416.2}{- 42} + \frac{48 c}{- 42}$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$b = \frac{- 416.2}{- 42} + \frac{48 c}{- 42}$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$b = \frac{- 416.2}{- 42} + \frac{48 c}{- 42}$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

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

Divide $- 416.2$ by $- 42$ .

$b = 9.9\overline{095238} + \frac{48 c}{- 42}$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.3.3.3.1.2

Cancel the common factor of $48$ and $- 42$ .

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Step 2.3.3.3.3.1.2.1

Factor $6$ out of $48 c$ .

$b = 9.9\overline{095238} + \frac{6 (8 c)}{- 42}$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.3.3.3.1.2.2

Cancel the common factors.

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Step 2.3.3.3.3.1.2.2.1

Factor $6$ out of $- 42$ .

$b = 9.9\overline{095238} + \frac{6 (8 c)}{6 (- 7)}$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.3.3.3.1.2.2.2

Cancel the common factor.

$b = 9.9\overline{095238} + \frac{6 (8 c)}{6 \cdot - 7}$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.3.3.3.1.2.2.3

Rewrite the expression.

$b = 9.9\overline{095238} + \frac{8 c}{- 7}$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$b = 9.9\overline{095238} + \frac{8 c}{- 7}$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$b = 9.9\overline{095238} + \frac{8 c}{- 7}$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.3.3.3.1.3

Move the negative in front of the fraction.

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 313.2 - 30 b - 35 c$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4

Replace all occurrences of $b$ with $9.9\overline{095238} - \frac{8 c}{7}$ in each equation.

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Step 2.3.4.1

Replace all occurrences of $b$ in $9.9 = 313.2 - 30 b - 35 c$ with $9.9\overline{095238} - \frac{8 c}{7}$ .

$9.9 = 313.2 - 30 (9.9\overline{095238} - \frac{8 c}{7}) - 35 c$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.2

Simplify the right side.

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Step 2.3.4.2.1

Simplify $313.2 - 30 (9.9\overline{095238} - \frac{8 c}{7}) - 35 c$ .

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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.

$9.9 = 313.2 - 30 \cdot 9.9\overline{095238} - 30 (- \frac{8 c}{7}) - 35 c$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.2.1.1.2

Multiply $- 30$ by $9.9\overline{095238}$ .

$9.9 = 313.2 - 297.\overline{285714} - 30 (- \frac{8 c}{7}) - 35 c$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.2.1.1.3

Multiply $- 30 (- \frac{8 c}{7})$ .

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Step 2.3.4.2.1.1.3.1

Multiply $- 1$ by $- 30$ .

$9.9 = 313.2 - 297.\overline{285714} + 30 (\frac{8 c}{7}) - 35 c$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.2.1.1.3.2

Combine $30$ and $\frac{8 c}{7}$ .

$9.9 = 313.2 - 297.\overline{285714} + \frac{30 (8 c)}{7} - 35 c$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.2.1.1.3.3

Multiply $8$ by $30$ .

$9.9 = 313.2 - 297.\overline{285714} + \frac{240 c}{7} - 35 c$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = 313.2 - 297.\overline{285714} + \frac{240 c}{7} - 35 c$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = 313.2 - 297.\overline{285714} + \frac{240 c}{7} - 35 c$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.2.1.2

Subtract $297.\overline{285714}$ from $313.2$ .

$9.9 = 15.9\overline{142857} + \frac{240 c}{7} - 35 c$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.2.1.3

To write $- 35 c$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$9.9 = 15.9\overline{142857} + \frac{240 c}{7} - 35 c \cdot \frac{7}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.2.1.4

Simplify terms.

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Step 2.3.4.2.1.4.1

Combine $- 35 c$ and $\frac{7}{7}$ .

$9.9 = 15.9\overline{142857} + \frac{240 c}{7} + \frac{- 35 c \cdot 7}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.2.1.4.2

Combine the numerators over the common denominator.

$9.9 = 15.9\overline{142857} + \frac{240 c - 35 c \cdot 7}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = 15.9\overline{142857} + \frac{240 c - 35 c \cdot 7}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.2.1.5

Simplify each term.

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Step 2.3.4.2.1.5.1

Simplify the numerator.

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Step 2.3.4.2.1.5.1.1

Factor $5 c$ out of $240 c - 35 c \cdot 7$ .

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Step 2.3.4.2.1.5.1.1.1

Factor $5 c$ out of $240 c$ .

$9.9 = 15.9\overline{142857} + \frac{5 c (48) - 35 c \cdot 7}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.2.1.5.1.1.2

Factor $5 c$ out of $- 35 c \cdot 7$ .

$9.9 = 15.9\overline{142857} + \frac{5 c (48) + 5 c (- 7 \cdot 7)}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.2.1.5.1.1.3

Factor $5 c$ out of $5 c (48) + 5 c (- 7 \cdot 7)$ .

$9.9 = 15.9\overline{142857} + \frac{5 c (48 - 7 \cdot 7)}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = 15.9\overline{142857} + \frac{5 c (48 - 7 \cdot 7)}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.2.1.5.1.2

Multiply $- 7$ by $7$ .

$9.9 = 15.9\overline{142857} + \frac{5 c (48 - 49)}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.2.1.5.1.3

Subtract $49$ from $48$ .

$9.9 = 15.9\overline{142857} + \frac{5 c \cdot - 1}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.2.1.5.1.4

Multiply $- 1$ by $5$ .

$9.9 = 15.9\overline{142857} + \frac{- 5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = 15.9\overline{142857} + \frac{- 5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.2.1.5.2

Move the negative in front of the fraction.

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 217.5 - 20 b - 24 c$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.3

Replace all occurrences of $b$ in $9.9 = 217.5 - 20 b - 24 c$ with $9.9\overline{095238} - \frac{8 c}{7}$ .

$9.9 = 217.5 - 20 (9.9\overline{095238} - \frac{8 c}{7}) - 24 c$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.4

Simplify the right side.

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Step 2.3.4.4.1

Simplify $217.5 - 20 (9.9\overline{095238} - \frac{8 c}{7}) - 24 c$ .

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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.

$9.9 = 217.5 - 20 \cdot 9.9\overline{095238} - 20 (- \frac{8 c}{7}) - 24 c$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.4.1.1.2

Multiply $- 20$ by $9.9\overline{095238}$ .

$9.9 = 217.5 - 198.\overline{190476} - 20 (- \frac{8 c}{7}) - 24 c$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.4.1.1.3

Multiply $- 20 (- \frac{8 c}{7})$ .

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Step 2.3.4.4.1.1.3.1

Multiply $- 1$ by $- 20$ .

$9.9 = 217.5 - 198.\overline{190476} + 20 (\frac{8 c}{7}) - 24 c$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.4.1.1.3.2

Combine $20$ and $\frac{8 c}{7}$ .

$9.9 = 217.5 - 198.\overline{190476} + \frac{20 (8 c)}{7} - 24 c$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.4.1.1.3.3

Multiply $8$ by $20$ .

$9.9 = 217.5 - 198.\overline{190476} + \frac{160 c}{7} - 24 c$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = 217.5 - 198.\overline{190476} + \frac{160 c}{7} - 24 c$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = 217.5 - 198.\overline{190476} + \frac{160 c}{7} - 24 c$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.4.1.2

Subtract $198.\overline{190476}$ from $217.5$ .

$9.9 = 19.3\overline{095238} + \frac{160 c}{7} - 24 c$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.4.1.3

To write $- 24 c$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$9.9 = 19.3\overline{095238} + \frac{160 c}{7} - 24 c \cdot \frac{7}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.4.1.4

Simplify terms.

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Step 2.3.4.4.1.4.1

Combine $- 24 c$ and $\frac{7}{7}$ .

$9.9 = 19.3\overline{095238} + \frac{160 c}{7} + \frac{- 24 c \cdot 7}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.4.1.4.2

Combine the numerators over the common denominator.

$9.9 = 19.3\overline{095238} + \frac{160 c - 24 c \cdot 7}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = 19.3\overline{095238} + \frac{160 c - 24 c \cdot 7}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.4.1.5

Simplify each term.

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Step 2.3.4.4.1.5.1

Simplify the numerator.

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Step 2.3.4.4.1.5.1.1

Factor $8 c$ out of $160 c - 24 c \cdot 7$ .

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Step 2.3.4.4.1.5.1.1.1

Factor $8 c$ out of $160 c$ .

$9.9 = 19.3\overline{095238} + \frac{8 c (20) - 24 c \cdot 7}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.4.1.5.1.1.2

Factor $8 c$ out of $- 24 c \cdot 7$ .

$9.9 = 19.3\overline{095238} + \frac{8 c (20) + 8 c (- 3 \cdot 7)}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.4.1.5.1.1.3

Factor $8 c$ out of $8 c (20) + 8 c (- 3 \cdot 7)$ .

$9.9 = 19.3\overline{095238} + \frac{8 c (20 - 3 \cdot 7)}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = 19.3\overline{095238} + \frac{8 c (20 - 3 \cdot 7)}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.4.1.5.1.2

Multiply $- 3$ by $7$ .

$9.9 = 19.3\overline{095238} + \frac{8 c (20 - 21)}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.4.1.5.1.3

Subtract $21$ from $20$ .

$9.9 = 19.3\overline{095238} + \frac{8 c \cdot - 1}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.4.1.5.1.4

Multiply $- 1$ by $8$ .

$9.9 = 19.3\overline{095238} + \frac{- 8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = 19.3\overline{095238} + \frac{- 8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.4.1.5.2

Move the negative in front of the fraction.

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 139.2 - 12 b - 15 c$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.5

Replace all occurrences of $b$ in $9.5 = 139.2 - 12 b - 15 c$ with $9.9\overline{095238} - \frac{8 c}{7}$ .

$9.5 = 139.2 - 12 (9.9\overline{095238} - \frac{8 c}{7}) - 15 c$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.6

Simplify the right side.

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Step 2.3.4.6.1

Simplify $139.2 - 12 (9.9\overline{095238} - \frac{8 c}{7}) - 15 c$ .

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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.

$9.5 = 139.2 - 12 \cdot 9.9\overline{095238} - 12 (- \frac{8 c}{7}) - 15 c$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.6.1.1.2

Multiply $- 12$ by $9.9\overline{095238}$ .

$9.5 = 139.2 - 118.9\overline{142857} - 12 (- \frac{8 c}{7}) - 15 c$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.6.1.1.3

Multiply $- 12 (- \frac{8 c}{7})$ .

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Step 2.3.4.6.1.1.3.1

Multiply $- 1$ by $- 12$ .

$9.5 = 139.2 - 118.9\overline{142857} + 12 (\frac{8 c}{7}) - 15 c$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.6.1.1.3.2

Combine $12$ and $\frac{8 c}{7}$ .

$9.5 = 139.2 - 118.9\overline{142857} + \frac{12 (8 c)}{7} - 15 c$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.6.1.1.3.3

Multiply $8$ by $12$ .

$9.5 = 139.2 - 118.9\overline{142857} + \frac{96 c}{7} - 15 c$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.5 = 139.2 - 118.9\overline{142857} + \frac{96 c}{7} - 15 c$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.5 = 139.2 - 118.9\overline{142857} + \frac{96 c}{7} - 15 c$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.6.1.2

Subtract $118.9\overline{142857}$ from $139.2$ .

$9.5 = 20.\overline{285714} + \frac{96 c}{7} - 15 c$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.6.1.3

To write $- 15 c$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$9.5 = 20.\overline{285714} + \frac{96 c}{7} - 15 c \cdot \frac{7}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.6.1.4

Simplify terms.

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Step 2.3.4.6.1.4.1

Combine $- 15 c$ and $\frac{7}{7}$ .

$9.5 = 20.\overline{285714} + \frac{96 c}{7} + \frac{- 15 c \cdot 7}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.6.1.4.2

Combine the numerators over the common denominator.

$9.5 = 20.\overline{285714} + \frac{96 c - 15 c \cdot 7}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.5 = 20.\overline{285714} + \frac{96 c - 15 c \cdot 7}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.6.1.5

Simplify each term.

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Step 2.3.4.6.1.5.1

Simplify the numerator.

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Step 2.3.4.6.1.5.1.1

Factor $3 c$ out of $96 c - 15 c \cdot 7$ .

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Step 2.3.4.6.1.5.1.1.1

Factor $3 c$ out of $96 c$ .

$9.5 = 20.\overline{285714} + \frac{3 c (32) - 15 c \cdot 7}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.6.1.5.1.1.2

Factor $3 c$ out of $- 15 c \cdot 7$ .

$9.5 = 20.\overline{285714} + \frac{3 c (32) + 3 c (- 5 \cdot 7)}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.6.1.5.1.1.3

Factor $3 c$ out of $3 c (32) + 3 c (- 5 \cdot 7)$ .

$9.5 = 20.\overline{285714} + \frac{3 c (32 - 5 \cdot 7)}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.5 = 20.\overline{285714} + \frac{3 c (32 - 5 \cdot 7)}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.6.1.5.1.2

Multiply $- 5$ by $7$ .

$9.5 = 20.\overline{285714} + \frac{3 c (32 - 35)}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.6.1.5.1.3

Subtract $35$ from $32$ .

$9.5 = 20.\overline{285714} + \frac{3 c \cdot - 3}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.6.1.5.1.4

Multiply $- 3$ by $3$ .

$9.5 = 20.\overline{285714} + \frac{- 9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.5 = 20.\overline{285714} + \frac{- 9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.6.1.5.2

Move the negative in front of the fraction.

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 78.3 - 6 b - 8 c$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.7

Replace all occurrences of $b$ in $9.2 = 78.3 - 6 b - 8 c$ with $9.9\overline{095238} - \frac{8 c}{7}$ .

$9.2 = 78.3 - 6 (9.9\overline{095238} - \frac{8 c}{7}) - 8 c$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.8

Simplify the right side.

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Step 2.3.4.8.1

Simplify $78.3 - 6 (9.9\overline{095238} - \frac{8 c}{7}) - 8 c$ .

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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.

$9.2 = 78.3 - 6 \cdot 9.9\overline{095238} - 6 (- \frac{8 c}{7}) - 8 c$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.8.1.1.2

Multiply $- 6$ by $9.9\overline{095238}$ .

$9.2 = 78.3 - 59.4\overline{571428} - 6 (- \frac{8 c}{7}) - 8 c$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.8.1.1.3

Multiply $- 6 (- \frac{8 c}{7})$ .

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Step 2.3.4.8.1.1.3.1

Multiply $- 1$ by $- 6$ .

$9.2 = 78.3 - 59.4\overline{571428} + 6 (\frac{8 c}{7}) - 8 c$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.8.1.1.3.2

Combine $6$ and $\frac{8 c}{7}$ .

$9.2 = 78.3 - 59.4\overline{571428} + \frac{6 (8 c)}{7} - 8 c$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.8.1.1.3.3

Multiply $8$ by $6$ .

$9.2 = 78.3 - 59.4\overline{571428} + \frac{48 c}{7} - 8 c$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.2 = 78.3 - 59.4\overline{571428} + \frac{48 c}{7} - 8 c$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.2 = 78.3 - 59.4\overline{571428} + \frac{48 c}{7} - 8 c$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.8.1.2

Subtract $59.4\overline{571428}$ from $78.3$ .

$9.2 = 18.8\overline{428571} + \frac{48 c}{7} - 8 c$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.8.1.3

To write $- 8 c$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$9.2 = 18.8\overline{428571} + \frac{48 c}{7} - 8 c \cdot \frac{7}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.8.1.4

Simplify terms.

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Step 2.3.4.8.1.4.1

Combine $- 8 c$ and $\frac{7}{7}$ .

$9.2 = 18.8\overline{428571} + \frac{48 c}{7} + \frac{- 8 c \cdot 7}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.8.1.4.2

Combine the numerators over the common denominator.

$9.2 = 18.8\overline{428571} + \frac{48 c - 8 c \cdot 7}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.2 = 18.8\overline{428571} + \frac{48 c - 8 c \cdot 7}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.8.1.5

Simplify each term.

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Step 2.3.4.8.1.5.1

Simplify the numerator.

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Step 2.3.4.8.1.5.1.1

Factor $8 c$ out of $48 c - 8 c \cdot 7$ .

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Step 2.3.4.8.1.5.1.1.1

Factor $8 c$ out of $48 c$ .

$9.2 = 18.8\overline{428571} + \frac{8 c (6) - 8 c \cdot 7}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.8.1.5.1.1.2

Factor $8 c$ out of $- 8 c \cdot 7$ .

$9.2 = 18.8\overline{428571} + \frac{8 c (6) + 8 c (- 1 \cdot 7)}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.8.1.5.1.1.3

Factor $8 c$ out of $8 c (6) + 8 c (- 1 \cdot 7)$ .

$9.2 = 18.8\overline{428571} + \frac{8 c (6 - 1 \cdot 7)}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.2 = 18.8\overline{428571} + \frac{8 c (6 - 1 \cdot 7)}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.8.1.5.1.2

Multiply $- 1$ by $7$ .

$9.2 = 18.8\overline{428571} + \frac{8 c (6 - 7)}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.8.1.5.1.3

Subtract $7$ from $6$ .

$9.2 = 18.8\overline{428571} + \frac{8 c \cdot - 1}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.8.1.5.1.4

Multiply $- 1$ by $8$ .

$9.2 = 18.8\overline{428571} + \frac{- 8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.2 = 18.8\overline{428571} + \frac{- 8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.8.1.5.2

Move the negative in front of the fraction.

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$8.7 = 34.8 - 2 b - 3 c$

$a = 8.7 - b - c$

Step 2.3.4.9

Replace all occurrences of $b$ in $8.7 = 34.8 - 2 b - 3 c$ with $9.9\overline{095238} - \frac{8 c}{7}$ .

$8.7 = 34.8 - 2 (9.9\overline{095238} - \frac{8 c}{7}) - 3 c$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - b - c$

Step 2.3.4.10

Simplify the right side.

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Step 2.3.4.10.1

Simplify $34.8 - 2 (9.9\overline{095238} - \frac{8 c}{7}) - 3 c$ .

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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.

$8.7 = 34.8 - 2 \cdot 9.9\overline{095238} - 2 (- \frac{8 c}{7}) - 3 c$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - b - c$

Step 2.3.4.10.1.1.2

Multiply $- 2$ by $9.9\overline{095238}$ .

$8.7 = 34.8 - 19.8\overline{190476} - 2 (- \frac{8 c}{7}) - 3 c$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - b - c$

Step 2.3.4.10.1.1.3

Multiply $- 2 (- \frac{8 c}{7})$ .

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Step 2.3.4.10.1.1.3.1

Multiply $- 1$ by $- 2$ .

$8.7 = 34.8 - 19.8\overline{190476} + 2 (\frac{8 c}{7}) - 3 c$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - b - c$

Step 2.3.4.10.1.1.3.2

Combine $2$ and $\frac{8 c}{7}$ .

$8.7 = 34.8 - 19.8\overline{190476} + \frac{2 (8 c)}{7} - 3 c$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - b - c$

Step 2.3.4.10.1.1.3.3

Multiply $8$ by $2$ .

$8.7 = 34.8 - 19.8\overline{190476} + \frac{16 c}{7} - 3 c$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - b - c$

$8.7 = 34.8 - 19.8\overline{190476} + \frac{16 c}{7} - 3 c$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - b - c$

$8.7 = 34.8 - 19.8\overline{190476} + \frac{16 c}{7} - 3 c$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - b - c$

Step 2.3.4.10.1.2

Subtract $19.8\overline{190476}$ from $34.8$ .

$8.7 = 14.9\overline{809523} + \frac{16 c}{7} - 3 c$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - b - c$

Step 2.3.4.10.1.3

To write $- 3 c$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$8.7 = 14.9\overline{809523} + \frac{16 c}{7} - 3 c \cdot \frac{7}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - b - c$

Step 2.3.4.10.1.4

Simplify terms.

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Step 2.3.4.10.1.4.1

Combine $- 3 c$ and $\frac{7}{7}$ .

$8.7 = 14.9\overline{809523} + \frac{16 c}{7} + \frac{- 3 c \cdot 7}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - b - c$

Step 2.3.4.10.1.4.2

Combine the numerators over the common denominator.

$8.7 = 14.9\overline{809523} + \frac{16 c - 3 c \cdot 7}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - b - c$

$8.7 = 14.9\overline{809523} + \frac{16 c - 3 c \cdot 7}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - b - c$

Step 2.3.4.10.1.5

Simplify each term.

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Step 2.3.4.10.1.5.1

Simplify the numerator.

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Step 2.3.4.10.1.5.1.1

Factor $c$ out of $16 c - 3 c \cdot 7$ .

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Step 2.3.4.10.1.5.1.1.1

Factor $c$ out of $16 c$ .

$8.7 = 14.9\overline{809523} + \frac{c \cdot 16 - 3 c \cdot 7}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - b - c$

Step 2.3.4.10.1.5.1.1.2

Factor $c$ out of $- 3 c \cdot 7$ .

$8.7 = 14.9\overline{809523} + \frac{c \cdot 16 + c (- 3 \cdot 7)}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - b - c$

Step 2.3.4.10.1.5.1.1.3

Factor $c$ out of $c \cdot 16 + c (- 3 \cdot 7)$ .

$8.7 = 14.9\overline{809523} + \frac{c (16 - 3 \cdot 7)}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - b - c$

$8.7 = 14.9\overline{809523} + \frac{c (16 - 3 \cdot 7)}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - b - c$

Step 2.3.4.10.1.5.1.2

Multiply $- 3$ by $7$ .

$8.7 = 14.9\overline{809523} + \frac{c (16 - 21)}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - b - c$

Step 2.3.4.10.1.5.1.3

Subtract $21$ from $16$ .

$8.7 = 14.9\overline{809523} + \frac{c \cdot - 5}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - b - c$

$8.7 = 14.9\overline{809523} + \frac{c \cdot - 5}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - b - c$

Step 2.3.4.10.1.5.2

Move $- 5$ to the left of $c$ .

$8.7 = 14.9\overline{809523} + \frac{- 5 \cdot c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - b - c$

Step 2.3.4.10.1.5.3

Move the negative in front of the fraction.

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - b - c$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - b - c$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - b - c$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - b - c$

Step 2.3.4.11

Replace all occurrences of $b$ in $a = 8.7 - b - c$ with $9.9\overline{095238} - \frac{8 c}{7}$ .

$a = 8.7 - (9.9\overline{095238} - \frac{8 c}{7}) - c$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.4.12

Simplify the right side.

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Step 2.3.4.12.1

Simplify $8.7 - (9.9\overline{095238} - \frac{8 c}{7}) - c$ .

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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.

$a = 8.7 - 1 \cdot 9.9\overline{095238} + \frac{8 c}{7} - c$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.4.12.1.1.2

Multiply $- 1$ by $9.9\overline{095238}$ .

$a = 8.7 - 9.9\overline{095238} + \frac{8 c}{7} - c$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.4.12.1.1.3

Multiply $- - \frac{8 c}{7}$ .

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Step 2.3.4.12.1.1.3.1

Multiply $- 1$ by $- 1$ .

$a = 8.7 - 9.9\overline{095238} + 1 (\frac{8 c}{7}) - c$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.4.12.1.1.3.2

Multiply $\frac{8 c}{7}$ by $1$ .

$a = 8.7 - 9.9\overline{095238} + \frac{8 c}{7} - c$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - 9.9\overline{095238} + \frac{8 c}{7} - c$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 8.7 - 9.9\overline{095238} + \frac{8 c}{7} - c$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.4.12.1.2

Subtract $9.9\overline{095238}$ from $8.7$ .

$a = - 1.2\overline{095238} + \frac{8 c}{7} - c$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.4.12.1.3

To write $- c$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$a = - 1.2\overline{095238} + \frac{8 c}{7} - c \cdot \frac{7}{7}$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.4.12.1.4

Simplify terms.

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Step 2.3.4.12.1.4.1

Combine $- c$ and $\frac{7}{7}$ .

$a = - 1.2\overline{095238} + \frac{8 c}{7} + \frac{- c \cdot 7}{7}$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.4.12.1.4.2

Combine the numerators over the common denominator.

$a = - 1.2\overline{095238} + \frac{8 c - c \cdot 7}{7}$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = - 1.2\overline{095238} + \frac{8 c - c \cdot 7}{7}$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.4.12.1.5

Simplify each term.

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Step 2.3.4.12.1.5.1

Simplify the numerator.

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Step 2.3.4.12.1.5.1.1

Factor $c$ out of $8 c - c \cdot 7$ .

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Step 2.3.4.12.1.5.1.1.1

Factor $c$ out of $8 c$ .

$a = - 1.2\overline{095238} + \frac{c \cdot 8 - c \cdot 7}{7}$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.4.12.1.5.1.1.2

Factor $c$ out of $- c \cdot 7$ .

$a = - 1.2\overline{095238} + \frac{c \cdot 8 + c (- 1 \cdot 7)}{7}$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.4.12.1.5.1.1.3

Factor $c$ out of $c \cdot 8 + c (- 1 \cdot 7)$ .

$a = - 1.2\overline{095238} + \frac{c (8 - 1 \cdot 7)}{7}$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = - 1.2\overline{095238} + \frac{c (8 - 1 \cdot 7)}{7}$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.4.12.1.5.1.2

Multiply $- 1$ by $7$ .

$a = - 1.2\overline{095238} + \frac{c (8 - 7)}{7}$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.4.12.1.5.1.3

Subtract $7$ from $8$ .

$a = - 1.2\overline{095238} + \frac{c \cdot 1}{7}$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = - 1.2\overline{095238} + \frac{c \cdot 1}{7}$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.4.12.1.5.2

Multiply $c$ by $1$ .

$a = - 1.2\overline{095238} + \frac{c}{7}$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$8.7 = 14.9\overline{809523} - \frac{5 c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.5

Solve for $c$ in $8.7 = 14.9\overline{809523} - \frac{5 c}{7}$ .

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Step 2.3.5.1

Rewrite the equation as $14.9\overline{809523} - \frac{5 c}{7} = 8.7$ .

$14.9\overline{809523} - \frac{5 c}{7} = 8.7$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.5.2

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

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Step 2.3.5.2.1

Subtract $14.9\overline{809523}$ from both sides of the equation.

$- \frac{5 c}{7} = 8.7 - 14.9\overline{809523}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.5.2.2

Subtract $14.9\overline{809523}$ from $8.7$ .

$- \frac{5 c}{7} = - 6.2\overline{809523}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$- \frac{5 c}{7} = - 6.2\overline{809523}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.5.3

Multiply both sides of the equation by $- \frac{7}{5}$ .

$- \frac{7}{5} \cdot (- \frac{5 c}{7}) = - \frac{7}{5} \cdot - 6.2\overline{809523}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.5.4

Simplify both sides of the equation.

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Step 2.3.5.4.1

Simplify the left side.

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Step 2.3.5.4.1.1

Simplify $- \frac{7}{5} (- \frac{5 c}{7})$ .

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Step 2.3.5.4.1.1.1

Cancel the common factor of $7$ .

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Step 2.3.5.4.1.1.1.1

Move the leading negative in $- \frac{7}{5}$ into the numerator.

$\frac{- 7}{5} \cdot (- \frac{5 c}{7}) = - \frac{7}{5} \cdot - 6.2\overline{809523}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.5.4.1.1.1.2

Move the leading negative in $- \frac{5 c}{7}$ into the numerator.

$\frac{- 7}{5} \cdot \frac{- 5 c}{7} = - \frac{7}{5} \cdot - 6.2\overline{809523}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.5.4.1.1.1.3

Factor $7$ out of $- 7$ .

$\frac{7 (- 1)}{5} \cdot \frac{- 5 c}{7} = - \frac{7}{5} \cdot - 6.2\overline{809523}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.5.4.1.1.1.4

Cancel the common factor.

$\frac{7 \cdot - 1}{5} \cdot \frac{- 5 c}{7} = - \frac{7}{5} \cdot - 6.2\overline{809523}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.5.4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{5} \cdot (- 5 c) = - \frac{7}{5} \cdot - 6.2\overline{809523}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$\frac{- 1}{5} \cdot (- 5 c) = - \frac{7}{5} \cdot - 6.2\overline{809523}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.5.4.1.1.2

Cancel the common factor of $5$ .

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Step 2.3.5.4.1.1.2.1

Factor $5$ out of $- 5 c$ .

$\frac{- 1}{5} \cdot (5 (- c)) = - \frac{7}{5} \cdot - 6.2\overline{809523}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.5.4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{5} \cdot (5 (- c)) = - \frac{7}{5} \cdot - 6.2\overline{809523}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.5.4.1.1.2.3

Rewrite the expression.

$c = - \frac{7}{5} \cdot - 6.2\overline{809523}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$c = - \frac{7}{5} \cdot - 6.2\overline{809523}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.5.4.1.1.3

Multiply.

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Step 2.3.5.4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 c = - \frac{7}{5} \cdot - 6.2\overline{809523}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.5.4.1.1.3.2

Multiply $c$ by $1$ .

$c = - \frac{7}{5} \cdot - 6.2\overline{809523}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$c = - \frac{7}{5} \cdot - 6.2\overline{809523}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$c = - \frac{7}{5} \cdot - 6.2\overline{809523}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$c = - \frac{7}{5} \cdot - 6.2\overline{809523}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.5.4.2

Simplify the right side.

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Step 2.3.5.4.2.1

Simplify $- \frac{7}{5} \cdot - 6.2\overline{809523}$ .

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Step 2.3.5.4.2.1.1

Multiply $- \frac{7}{5} \cdot - 6.2\overline{809523}$ .

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Step 2.3.5.4.2.1.1.1

Multiply $- 6.2\overline{809523}$ by $- 1$ .

$c = 6.2\overline{809523} (\frac{7}{5})$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.5.4.2.1.1.2

Combine $6.2\overline{809523}$ and $\frac{7}{5}$ .

$c = \frac{6.2\overline{809523} \cdot 7}{5}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.5.4.2.1.1.3

Multiply $6.2\overline{809523}$ by $7$ .

$c = \frac{43.9\overline{6}}{5}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$c = \frac{43.9\overline{6}}{5}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.5.4.2.1.2

Divide $43.9\overline{6}$ by $5$ .

$c = 8.79\overline{3}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$c = 8.79\overline{3}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$c = 8.79\overline{3}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$c = 8.79\overline{3}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$c = 8.79\overline{3}$

$a = - 1.2\overline{095238} + \frac{c}{7}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.6

Replace all occurrences of $c$ with $8.79\overline{3}$ in each equation.

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Step 2.3.6.1

Replace all occurrences of $c$ in $a = - 1.2\overline{095238} + \frac{c}{7}$ with $8.79\overline{3}$ .

$a = - 1.2\overline{095238} + \frac{8.79\overline{3}}{7}$

$c = 8.79\overline{3}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.6.2

Simplify the right side.

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Step 2.3.6.2.1

Simplify $- 1.2\overline{095238} + \frac{8.79\overline{3}}{7}$ .

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Step 2.3.6.2.1.1

Divide $8.79\overline{3}$ by $7$ .

$a = - 1.2\overline{095238} + 1.25619047$

$c = 8.79\overline{3}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.6.2.1.2

Add $- 1.2\overline{095238}$ and $1.25619047$ .

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.2 = 18.8\overline{428571} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.6.3

Replace all occurrences of $c$ in $9.2 = 18.8\overline{428571} - \frac{8 c}{7}$ with $8.79\overline{3}$ .

$9.2 = 18.8\overline{428571} - \frac{8 (8.79\overline{3})}{7}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.6.4

Simplify the right side.

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Step 2.3.6.4.1

Simplify $18.8\overline{428571} - \frac{8 (8.79\overline{3})}{7}$ .

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Step 2.3.6.4.1.1

Simplify each term.

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Step 2.3.6.4.1.1.1

Multiply $8$ by $8.79\overline{3}$ .

$9.2 = 18.8\overline{428571} - \frac{70.34666666}{7}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.6.4.1.1.2

Divide $70.34666666$ by $7$ .

$9.2 = 18.8\overline{428571} - 1 \cdot 10.0495238$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.6.4.1.1.3

Multiply $- 1$ by $10.0495238$ .

$9.2 = 18.8\overline{428571} - 10.0495238$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 18.8\overline{428571} - 10.0495238$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.6.4.1.2

Subtract $10.0495238$ from $18.8\overline{428571}$ .

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.5 = 20.\overline{285714} - \frac{9 c}{7}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.6.5

Replace all occurrences of $c$ in $9.5 = 20.\overline{285714} - \frac{9 c}{7}$ with $8.79\overline{3}$ .

$9.5 = 20.\overline{285714} - \frac{9 (8.79\overline{3})}{7}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.6.6

Simplify the right side.

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Step 2.3.6.6.1

Simplify $20.\overline{285714} - \frac{9 (8.79\overline{3})}{7}$ .

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Step 2.3.6.6.1.1

Simplify each term.

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Step 2.3.6.6.1.1.1

Multiply $9$ by $8.79\overline{3}$ .

$9.5 = 20.\overline{285714} - \frac{79.14}{7}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.6.6.1.1.2

Divide $79.14$ by $7$ .

$9.5 = 20.\overline{285714} - 1 \cdot 11.30571428$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.6.6.1.1.3

Multiply $- 1$ by $11.30571428$ .

$9.5 = 20.\overline{285714} - 11.30571428$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 20.\overline{285714} - 11.30571428$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.6.6.1.2

Subtract $11.30571428$ from $20.\overline{285714}$ .

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.9 = 19.3\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.6.7

Replace all occurrences of $c$ in $9.9 = 19.3\overline{095238} - \frac{8 c}{7}$ with $8.79\overline{3}$ .

$9.9 = 19.3\overline{095238} - \frac{8 (8.79\overline{3})}{7}$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.6.8

Simplify the right side.

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Step 2.3.6.8.1

Simplify $19.3\overline{095238} - \frac{8 (8.79\overline{3})}{7}$ .

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Step 2.3.6.8.1.1

Simplify each term.

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Step 2.3.6.8.1.1.1

Multiply $8$ by $8.79\overline{3}$ .

$9.9 = 19.3\overline{095238} - \frac{70.34666666}{7}$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.6.8.1.1.2

Divide $70.34666666$ by $7$ .

$9.9 = 19.3\overline{095238} - 1 \cdot 10.0495238$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.6.8.1.1.3

Multiply $- 1$ by $10.0495238$ .

$9.9 = 19.3\overline{095238} - 10.0495238$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 19.3\overline{095238} - 10.0495238$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.6.8.1.2

Subtract $10.0495238$ from $19.3\overline{095238}$ .

$9.9 = 9.25\overline{9}$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 9.25\overline{9}$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 9.25\overline{9}$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$9.9 = 15.9\overline{142857} - \frac{5 c}{7}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.6.9

Replace all occurrences of $c$ in $9.9 = 15.9\overline{142857} - \frac{5 c}{7}$ with $8.79\overline{3}$ .

$9.9 = 15.9\overline{142857} - \frac{5 (8.79\overline{3})}{7}$

$9.9 = 9.25\overline{9}$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.6.10

Simplify the right side.

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Step 2.3.6.10.1

Simplify $15.9\overline{142857} - \frac{5 (8.79\overline{3})}{7}$ .

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Step 2.3.6.10.1.1

Simplify each term.

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Step 2.3.6.10.1.1.1

Multiply $5$ by $8.79\overline{3}$ .

$9.9 = 15.9\overline{142857} - \frac{43.9\overline{6}}{7}$

$9.9 = 9.25\overline{9}$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.6.10.1.1.2

Divide $43.9\overline{6}$ by $7$ .

$9.9 = 15.9\overline{142857} - 1 \cdot 6.2\overline{809523}$

$9.9 = 9.25\overline{9}$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.6.10.1.1.3

Multiply $- 1$ by $6.2\overline{809523}$ .

$9.9 = 15.9\overline{142857} - 6.2\overline{809523}$

$9.9 = 9.25\overline{9}$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 15.9\overline{142857} - 6.2\overline{809523}$

$9.9 = 9.25\overline{9}$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.6.10.1.2

Subtract $6.2\overline{809523}$ from $15.9\overline{142857}$ .

$9.9 = 9.6\overline{3}$

$9.9 = 9.25\overline{9}$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.25\overline{9}$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.25\overline{9}$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$b = 9.9\overline{095238} - \frac{8 c}{7}$

Step 2.3.6.11

Replace all occurrences of $c$ in $b = 9.9\overline{095238} - \frac{8 c}{7}$ with $8.79\overline{3}$ .

$b = 9.9\overline{095238} - \frac{8 (8.79\overline{3})}{7}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.25\overline{9}$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

Step 2.3.6.12

Simplify the right side.

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Step 2.3.6.12.1

Simplify $9.9\overline{095238} - \frac{8 (8.79\overline{3})}{7}$ .

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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 $8$ by $8.79\overline{3}$ .

$b = 9.9\overline{095238} - \frac{70.34666666}{7}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.25\overline{9}$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

Step 2.3.6.12.1.1.2

Divide $70.34666666$ by $7$ .

$b = 9.9\overline{095238} - 1 \cdot 10.0495238$

$9.9 = 9.6\overline{3}$

$9.9 = 9.25\overline{9}$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

Step 2.3.6.12.1.1.3

Multiply $- 1$ by $10.0495238$ .

$b = 9.9\overline{095238} - 10.0495238$

$9.9 = 9.6\overline{3}$

$9.9 = 9.25\overline{9}$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$b = 9.9\overline{095238} - 10.0495238$

$9.9 = 9.6\overline{3}$

$9.9 = 9.25\overline{9}$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

Step 2.3.6.12.1.2

Subtract $10.0495238$ from $9.9\overline{095238}$ .

$b = - 0.13\overline{9}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.25\overline{9}$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$b = - 0.13\overline{9}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.25\overline{9}$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$b = - 0.13\overline{9}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.25\overline{9}$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

$b = - 0.13\overline{9}$

$9.9 = 9.6\overline{3}$

$9.9 = 9.25\overline{9}$

$9.5 = 8.97\overline{9}$

$9.2 = 8.79\overline{3}$

$a = 0.04\overline{6}$

$c = 8.79\overline{3}$

Step 2.3.7

Since $9.9 = 9.6\overline{3}$ 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 $x = 1$ .

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Step 2.4.1.1

Simplify each term.

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Step 2.4.1.1.1

One to any power is one.

$y = 0 \cdot 1 + (0) \cdot (1) + 0$

Step 2.4.1.1.2

Multiply $0$ by $1$ .

$y = 0 + (0) \cdot (1) + 0$

Step 2.4.1.1.3

Multiply $0$ by $1$ .

$y = 0 + 0 + 0$

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, $x = 1$ . This check does not pass, since $y = 0$ and $y = 8.7$ . The function rule can't be quadratic.

$0 \neq 8.7$

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 $a$ in $8.7 = a + b + c + d$ .

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Step 3.3.1.1

Rewrite the equation as $a + b + c + d = 8.7$ .

$a + b + c + d = 8.7$

$8.7 = a \cdot 2^{3} + b + c + d$

$9.2 = a \cdot 3^{3} + b + c + d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.1.2

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

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Step 3.3.1.2.1

Subtract $b$ from both sides of the equation.

$a + c + d = 8.7 - b$

$8.7 = a \cdot 2^{3} + b + c + d$

$9.2 = a \cdot 3^{3} + b + c + d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.1.2.2

Subtract $c$ from both sides of the equation.

$a + d = 8.7 - b - c$

$8.7 = a \cdot 2^{3} + b + c + d$

$9.2 = a \cdot 3^{3} + b + c + d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.1.2.3

Subtract $d$ from both sides of the equation.

$a = 8.7 - b - c - d$

$8.7 = a \cdot 2^{3} + b + c + d$

$9.2 = a \cdot 3^{3} + b + c + d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

$a = 8.7 - b - c - d$

$8.7 = a \cdot 2^{3} + b + c + d$

$9.2 = a \cdot 3^{3} + b + c + d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

$a = 8.7 - b - c - d$

$8.7 = a \cdot 2^{3} + b + c + d$

$9.2 = a \cdot 3^{3} + b + c + d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2

Replace all occurrences of $a$ with $8.7 - b - c - d$ in each equation.

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Step 3.3.2.1

Replace all occurrences of $a$ in $8.7 = a \cdot 2^{3} + b + c + d$ with $8.7 - b - c - d$ .

$8.7 = (8.7 - b - c - d) \cdot 2^{3} + b + c + d$

$a = 8.7 - b - c - d$

$9.2 = a \cdot 3^{3} + b + c + d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.2

Simplify the right side.

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Step 3.3.2.2.1

Simplify $(8.7 - b - c - d) \cdot 2^{3} + b + c + d$ .

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Step 3.3.2.2.1.1

Simplify each term.

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Step 3.3.2.2.1.1.1

Raise $2$ to the power of $3$ .

$8.7 = (8.7 - b - c - d) \cdot 8 + b + c + d$

$a = 8.7 - b - c - d$

$9.2 = a \cdot 3^{3} + b + c + d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.2.1.1.2

Apply the distributive property.

$8.7 = 8.7 \cdot 8 - b \cdot 8 - c \cdot 8 - d \cdot 8 + b + c + d$

$a = 8.7 - b - c - d$

$9.2 = a \cdot 3^{3} + b + c + d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.2.1.1.3

Simplify.

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Step 3.3.2.2.1.1.3.1

Multiply $8.7$ by $8$ .

$8.7 = 69.6 - b \cdot 8 - c \cdot 8 - d \cdot 8 + b + c + d$

$a = 8.7 - b - c - d$

$9.2 = a \cdot 3^{3} + b + c + d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.2.1.1.3.2

Multiply $8$ by $- 1$ .

$8.7 = 69.6 - 8 b - c \cdot 8 - d \cdot 8 + b + c + d$

$a = 8.7 - b - c - d$

$9.2 = a \cdot 3^{3} + b + c + d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.2.1.1.3.3

Multiply $8$ by $- 1$ .

$8.7 = 69.6 - 8 b - 8 c - d \cdot 8 + b + c + d$

$a = 8.7 - b - c - d$

$9.2 = a \cdot 3^{3} + b + c + d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.2.1.1.3.4

Multiply $8$ by $- 1$ .

$8.7 = 69.6 - 8 b - 8 c - 8 d + b + c + d$

$a = 8.7 - b - c - d$

$9.2 = a \cdot 3^{3} + b + c + d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

$8.7 = 69.6 - 8 b - 8 c - 8 d + b + c + d$

$a = 8.7 - b - c - d$

$9.2 = a \cdot 3^{3} + b + c + d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

$8.7 = 69.6 - 8 b - 8 c - 8 d + b + c + d$

$a = 8.7 - b - c - d$

$9.2 = a \cdot 3^{3} + b + c + d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.2.1.2

Simplify by adding terms.

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Step 3.3.2.2.1.2.1

Add $- 8 b$ and $b$ .

$8.7 = 69.6 - 7 b - 8 c - 8 d + c + d$

$a = 8.7 - b - c - d$

$9.2 = a \cdot 3^{3} + b + c + d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.2.1.2.2

Add $- 8 c$ and $c$ .

$8.7 = 69.6 - 7 b - 7 c - 8 d + d$

$a = 8.7 - b - c - d$

$9.2 = a \cdot 3^{3} + b + c + d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.2.1.2.3

Add $- 8 d$ and $d$ .

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.2 = a \cdot 3^{3} + b + c + d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.2 = a \cdot 3^{3} + b + c + d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.2 = a \cdot 3^{3} + b + c + d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.2 = a \cdot 3^{3} + b + c + d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.3

Replace all occurrences of $a$ in $9.2 = a \cdot 3^{3} + b + c + d$ with $8.7 - b - c - d$ .

$9.2 = (8.7 - b - c - d) \cdot 3^{3} + b + c + d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.4

Simplify the right side.

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Step 3.3.2.4.1

Simplify $(8.7 - b - c - d) \cdot 3^{3} + b + c + d$ .

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Step 3.3.2.4.1.1

Simplify each term.

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Step 3.3.2.4.1.1.1

Raise $3$ to the power of $3$ .

$9.2 = (8.7 - b - c - d) \cdot 27 + b + c + d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.4.1.1.2

Apply the distributive property.

$9.2 = 8.7 \cdot 27 - b \cdot 27 - c \cdot 27 - d \cdot 27 + b + c + d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.4.1.1.3

Simplify.

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Step 3.3.2.4.1.1.3.1

Multiply $8.7$ by $27$ .

$9.2 = 234.9 - b \cdot 27 - c \cdot 27 - d \cdot 27 + b + c + d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.4.1.1.3.2

Multiply $27$ by $- 1$ .

$9.2 = 234.9 - 27 b - c \cdot 27 - d \cdot 27 + b + c + d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.4.1.1.3.3

Multiply $27$ by $- 1$ .

$9.2 = 234.9 - 27 b - 27 c - d \cdot 27 + b + c + d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.4.1.1.3.4

Multiply $27$ by $- 1$ .

$9.2 = 234.9 - 27 b - 27 c - 27 d + b + c + d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

$9.2 = 234.9 - 27 b - 27 c - 27 d + b + c + d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

$9.2 = 234.9 - 27 b - 27 c - 27 d + b + c + d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.4.1.2

Simplify by adding terms.

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Step 3.3.2.4.1.2.1

Add $- 27 b$ and $b$ .

$9.2 = 234.9 - 26 b - 27 c - 27 d + c + d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.4.1.2.2

Add $- 27 c$ and $c$ .

$9.2 = 234.9 - 26 b - 26 c - 27 d + d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.4.1.2.3

Add $- 27 d$ and $d$ .

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.5 = a \cdot 4^{3} + b + c + d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.5

Replace all occurrences of $a$ in $9.5 = a \cdot 4^{3} + b + c + d$ with $8.7 - b - c - d$ .

$9.5 = (8.7 - b - c - d) \cdot 4^{3} + b + c + d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.6

Simplify the right side.

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Step 3.3.2.6.1

Simplify $(8.7 - b - c - d) \cdot 4^{3} + b + c + d$ .

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Step 3.3.2.6.1.1

Simplify each term.

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Step 3.3.2.6.1.1.1

Raise $4$ to the power of $3$ .

$9.5 = (8.7 - b - c - d) \cdot 64 + b + c + d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.6.1.1.2

Apply the distributive property.

$9.5 = 8.7 \cdot 64 - b \cdot 64 - c \cdot 64 - d \cdot 64 + b + c + d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.6.1.1.3

Simplify.

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Step 3.3.2.6.1.1.3.1

Multiply $8.7$ by $64$ .

$9.5 = 556.8 - b \cdot 64 - c \cdot 64 - d \cdot 64 + b + c + d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.6.1.1.3.2

Multiply $64$ by $- 1$ .

$9.5 = 556.8 - 64 b - c \cdot 64 - d \cdot 64 + b + c + d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.6.1.1.3.3

Multiply $64$ by $- 1$ .

$9.5 = 556.8 - 64 b - 64 c - d \cdot 64 + b + c + d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.6.1.1.3.4

Multiply $64$ by $- 1$ .

$9.5 = 556.8 - 64 b - 64 c - 64 d + b + c + d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

$9.5 = 556.8 - 64 b - 64 c - 64 d + b + c + d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

$9.5 = 556.8 - 64 b - 64 c - 64 d + b + c + d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.6.1.2

Simplify by adding terms.

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Step 3.3.2.6.1.2.1

Add $- 64 b$ and $b$ .

$9.5 = 556.8 - 63 b - 64 c - 64 d + c + d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.6.1.2.2

Add $- 64 c$ and $c$ .

$9.5 = 556.8 - 63 b - 63 c - 64 d + d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.6.1.2.3

Add $- 64 d$ and $d$ .

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 5^{3} + b + c + d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.7

Replace all occurrences of $a$ in $9.9 = a \cdot 5^{3} + b + c + d$ with $8.7 - b - c - d$ .

$9.9 = (8.7 - b - c - d) \cdot 5^{3} + b + c + d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.8

Simplify the right side.

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Step 3.3.2.8.1

Simplify $(8.7 - b - c - d) \cdot 5^{3} + b + c + d$ .

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Step 3.3.2.8.1.1

Simplify each term.

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Step 3.3.2.8.1.1.1

Raise $5$ to the power of $3$ .

$9.9 = (8.7 - b - c - d) \cdot 125 + b + c + d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.8.1.1.2

Apply the distributive property.

$9.9 = 8.7 \cdot 125 - b \cdot 125 - c \cdot 125 - d \cdot 125 + b + c + d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.8.1.1.3

Simplify.

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Step 3.3.2.8.1.1.3.1

Multiply $8.7$ by $125$ .

$9.9 = 1087.5 - b \cdot 125 - c \cdot 125 - d \cdot 125 + b + c + d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.8.1.1.3.2

Multiply $125$ by $- 1$ .

$9.9 = 1087.5 - 125 b - c \cdot 125 - d \cdot 125 + b + c + d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.8.1.1.3.3

Multiply $125$ by $- 1$ .

$9.9 = 1087.5 - 125 b - 125 c - d \cdot 125 + b + c + d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.8.1.1.3.4

Multiply $125$ by $- 1$ .

$9.9 = 1087.5 - 125 b - 125 c - 125 d + b + c + d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

$9.9 = 1087.5 - 125 b - 125 c - 125 d + b + c + d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

$9.9 = 1087.5 - 125 b - 125 c - 125 d + b + c + d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.8.1.2

Simplify by adding terms.

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Step 3.3.2.8.1.2.1

Add $- 125 b$ and $b$ .

$9.9 = 1087.5 - 124 b - 125 c - 125 d + c + d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.8.1.2.2

Add $- 125 c$ and $c$ .

$9.9 = 1087.5 - 124 b - 124 c - 125 d + d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.8.1.2.3

Add $- 125 d$ and $d$ .

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = a \cdot 6^{3} + b + c + d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.9

Replace all occurrences of $a$ in $9.9 = a \cdot 6^{3} + b + c + d$ with $8.7 - b - c - d$ .

$9.9 = (8.7 - b - c - d) \cdot 6^{3} + b + c + d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.10

Simplify the right side.

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Step 3.3.2.10.1

Simplify $(8.7 - b - c - d) \cdot 6^{3} + b + c + d$ .

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Step 3.3.2.10.1.1

Simplify each term.

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Step 3.3.2.10.1.1.1

Raise $6$ to the power of $3$ .

$9.9 = (8.7 - b - c - d) \cdot 216 + b + c + d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.10.1.1.2

Apply the distributive property.

$9.9 = 8.7 \cdot 216 - b \cdot 216 - c \cdot 216 - d \cdot 216 + b + c + d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.10.1.1.3

Simplify.

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Step 3.3.2.10.1.1.3.1

Multiply $8.7$ by $216$ .

$9.9 = 1879.2 - b \cdot 216 - c \cdot 216 - d \cdot 216 + b + c + d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.10.1.1.3.2

Multiply $216$ by $- 1$ .

$9.9 = 1879.2 - 216 b - c \cdot 216 - d \cdot 216 + b + c + d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.10.1.1.3.3

Multiply $216$ by $- 1$ .

$9.9 = 1879.2 - 216 b - 216 c - d \cdot 216 + b + c + d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.10.1.1.3.4

Multiply $216$ by $- 1$ .

$9.9 = 1879.2 - 216 b - 216 c - 216 d + b + c + d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$10.1 = a \cdot 7^{3} + b + c + d$

$9.9 = 1879.2 - 216 b - 216 c - 216 d + b + c + d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$10.1 = a \cdot 7^{3} + b + c + d$

$9.9 = 1879.2 - 216 b - 216 c - 216 d + b + c + d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.10.1.2

Simplify by adding terms.

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Step 3.3.2.10.1.2.1

Add $- 216 b$ and $b$ .

$9.9 = 1879.2 - 215 b - 216 c - 216 d + c + d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.10.1.2.2

Add $- 216 c$ and $c$ .

$9.9 = 1879.2 - 215 b - 215 c - 216 d + d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.10.1.2.3

Add $- 216 d$ and $d$ .

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$10.1 = a \cdot 7^{3} + b + c + d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$10.1 = a \cdot 7^{3} + b + c + d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$10.1 = a \cdot 7^{3} + b + c + d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$10.1 = a \cdot 7^{3} + b + c + d$

Step 3.3.2.11

Replace all occurrences of $a$ in $10.1 = a \cdot 7^{3} + b + c + d$ with $8.7 - b - c - d$ .

$10.1 = (8.7 - b - c - d) \cdot 7^{3} + b + c + d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.2.12

Simplify the right side.

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Step 3.3.2.12.1

Simplify $(8.7 - b - c - d) \cdot 7^{3} + b + c + d$ .

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Step 3.3.2.12.1.1

Simplify each term.

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Step 3.3.2.12.1.1.1

Raise $7$ to the power of $3$ .

$10.1 = (8.7 - b - c - d) \cdot 343 + b + c + d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.2.12.1.1.2

Apply the distributive property.

$10.1 = 8.7 \cdot 343 - b \cdot 343 - c \cdot 343 - d \cdot 343 + b + c + d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.2.12.1.1.3

Simplify.

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Step 3.3.2.12.1.1.3.1

Multiply $8.7$ by $343$ .

$10.1 = 2984.1 - b \cdot 343 - c \cdot 343 - d \cdot 343 + b + c + d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.2.12.1.1.3.2

Multiply $343$ by $- 1$ .

$10.1 = 2984.1 - 343 b - c \cdot 343 - d \cdot 343 + b + c + d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.2.12.1.1.3.3

Multiply $343$ by $- 1$ .

$10.1 = 2984.1 - 343 b - 343 c - d \cdot 343 + b + c + d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.2.12.1.1.3.4

Multiply $343$ by $- 1$ .

$10.1 = 2984.1 - 343 b - 343 c - 343 d + b + c + d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$10.1 = 2984.1 - 343 b - 343 c - 343 d + b + c + d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$10.1 = 2984.1 - 343 b - 343 c - 343 d + b + c + d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.2.12.1.2

Simplify by adding terms.

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Step 3.3.2.12.1.2.1

Add $- 343 b$ and $b$ .

$10.1 = 2984.1 - 342 b - 343 c - 343 d + c + d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.2.12.1.2.2

Add $- 343 c$ and $c$ .

$10.1 = 2984.1 - 342 b - 342 c - 343 d + d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.2.12.1.2.3

Add $- 343 d$ and $d$ .

$10.1 = 2984.1 - 342 b - 342 c - 342 d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$10.1 = 2984.1 - 342 b - 342 c - 342 d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$10.1 = 2984.1 - 342 b - 342 c - 342 d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$10.1 = 2984.1 - 342 b - 342 c - 342 d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$10.1 = 2984.1 - 342 b - 342 c - 342 d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.3

Solve for $b$ in $10.1 = 2984.1 - 342 b - 342 c - 342 d$ .

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Step 3.3.3.1

Rewrite the equation as $2984.1 - 342 b - 342 c - 342 d = 10.1$ .

$2984.1 - 342 b - 342 c - 342 d = 10.1$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.3.2

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

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Step 3.3.3.2.1

Subtract $2984.1$ from both sides of the equation.

$- 342 b - 342 c - 342 d = 10.1 - 2984.1$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.3.2.2

Add $342 c$ to both sides of the equation.

$- 342 b - 342 d = 10.1 - 2984.1 + 342 c$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.3.2.3

Add $342 d$ to both sides of the equation.

$- 342 b = 10.1 - 2984.1 + 342 c + 342 d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.3.2.4

Subtract $2984.1$ from $10.1$ .

$- 342 b = - 2974 + 342 c + 342 d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$- 342 b = - 2974 + 342 c + 342 d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.3.3

Divide each term in $- 342 b = - 2974 + 342 c + 342 d$ by $- 342$ and simplify.

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Step 3.3.3.3.1

Divide each term in $- 342 b = - 2974 + 342 c + 342 d$ by $- 342$ .

$\frac{- 342 b}{- 342} = \frac{- 2974}{- 342} + \frac{342 c}{- 342} + \frac{342 d}{- 342}$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

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 $- 342$ .

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Step 3.3.3.3.2.1.1

Cancel the common factor.

$\frac{- 342 b}{- 342} = \frac{- 2974}{- 342} + \frac{342 c}{- 342} + \frac{342 d}{- 342}$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.3.3.2.1.2

Divide $b$ by $1$ .

$b = \frac{- 2974}{- 342} + \frac{342 c}{- 342} + \frac{342 d}{- 342}$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$b = \frac{- 2974}{- 342} + \frac{342 c}{- 342} + \frac{342 d}{- 342}$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$b = \frac{- 2974}{- 342} + \frac{342 c}{- 342} + \frac{342 d}{- 342}$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.3.3.3

Simplify the right side.

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Step 3.3.3.3.3.1

Simplify each term.

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Step 3.3.3.3.3.1.1

Cancel the common factor of $- 2974$ and $- 342$ .

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Step 3.3.3.3.3.1.1.1

Factor $- 2$ out of $- 2974$ .

$b = \frac{- 2 \cdot 1487}{- 342} + \frac{342 c}{- 342} + \frac{342 d}{- 342}$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.3.3.3.1.1.2

Cancel the common factors.

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Step 3.3.3.3.3.1.1.2.1

Factor $- 2$ out of $- 342$ .

$b = \frac{- 2 \cdot 1487}{- 2 \cdot 171} + \frac{342 c}{- 342} + \frac{342 d}{- 342}$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.3.3.3.1.1.2.2

Cancel the common factor.

$b = \frac{- 2 \cdot 1487}{- 2 \cdot 171} + \frac{342 c}{- 342} + \frac{342 d}{- 342}$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.3.3.3.1.1.2.3

Rewrite the expression.

$b = \frac{1487}{171} + \frac{342 c}{- 342} + \frac{342 d}{- 342}$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$b = \frac{1487}{171} + \frac{342 c}{- 342} + \frac{342 d}{- 342}$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$b = \frac{1487}{171} + \frac{342 c}{- 342} + \frac{342 d}{- 342}$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.3.3.3.1.2

Cancel the common factor of $342$ and $- 342$ .

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Step 3.3.3.3.3.1.2.1

Factor $342$ out of $342 c$ .

$b = \frac{1487}{171} + \frac{342 (c)}{- 342} + \frac{342 d}{- 342}$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.3.3.3.1.2.2

Move the negative one from the denominator of $\frac{c}{- 1}$ .

$b = \frac{1487}{171} - 1 \cdot c + \frac{342 d}{- 342}$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$b = \frac{1487}{171} - 1 \cdot c + \frac{342 d}{- 342}$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.3.3.3.1.3

Rewrite $- 1 \cdot c$ as $- c$ .

$b = \frac{1487}{171} - c + \frac{342 d}{- 342}$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.3.3.3.1.4

Cancel the common factor of $342$ and $- 342$ .

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Step 3.3.3.3.3.1.4.1

Factor $342$ out of $342 d$ .

$b = \frac{1487}{171} - c + \frac{342 (d)}{- 342}$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.3.3.3.1.4.2

Move the negative one from the denominator of $\frac{d}{- 1}$ .

$b = \frac{1487}{171} - c - 1 \cdot d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$b = \frac{1487}{171} - c - 1 \cdot d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.3.3.3.1.5

Rewrite $- 1 \cdot d$ as $- d$ .

$b = \frac{1487}{171} - c - d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$b = \frac{1487}{171} - c - d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$b = \frac{1487}{171} - c - d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$b = \frac{1487}{171} - c - d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$b = \frac{1487}{171} - c - d$

$9.9 = 1879.2 - 215 b - 215 c - 215 d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4

Replace all occurrences of $b$ with $\frac{1487}{171} - c - d$ in each equation.

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Step 3.3.4.1

Replace all occurrences of $b$ in $9.9 = 1879.2 - 215 b - 215 c - 215 d$ with $\frac{1487}{171} - c - d$ .

$9.9 = 1879.2 - 215 (\frac{1487}{171} - c - d) - 215 c - 215 d$

$b = \frac{1487}{171} - c - d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.2

Simplify the right side.

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Step 3.3.4.2.1

Simplify $1879.2 - 215 (\frac{1487}{171} - c - d) - 215 c - 215 d$ .

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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

Apply the distributive property.

$9.9 = 1879.2 - 215 (\frac{1487}{171}) - 215 (- c) - 215 (- d) - 215 c - 215 d$

$b = \frac{1487}{171} - c - d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.2.1.1.2

Simplify.

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Step 3.3.4.2.1.1.2.1

Multiply $- 215 (\frac{1487}{171})$ .

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Step 3.3.4.2.1.1.2.1.1

Combine $- 215$ and $\frac{1487}{171}$ .

$9.9 = 1879.2 + \frac{- 215 \cdot 1487}{171} - 215 (- c) - 215 (- d) - 215 c - 215 d$

$b = \frac{1487}{171} - c - d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.2.1.1.2.1.2

Multiply $- 215$ by $1487$ .

$9.9 = 1879.2 + \frac{- 319705}{171} - 215 (- c) - 215 (- d) - 215 c - 215 d$

$b = \frac{1487}{171} - c - d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = 1879.2 + \frac{- 319705}{171} - 215 (- c) - 215 (- d) - 215 c - 215 d$

$b = \frac{1487}{171} - c - d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.2.1.1.2.2

Multiply $- 1$ by $- 215$ .

$9.9 = 1879.2 + \frac{- 319705}{171} + 215 c - 215 (- d) - 215 c - 215 d$

$b = \frac{1487}{171} - c - d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.2.1.1.2.3

Multiply $- 1$ by $- 215$ .

$9.9 = 1879.2 + \frac{- 319705}{171} + 215 c + 215 d - 215 c - 215 d$

$b = \frac{1487}{171} - c - d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = 1879.2 + \frac{- 319705}{171} + 215 c + 215 d - 215 c - 215 d$

$b = \frac{1487}{171} - c - d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.2.1.1.3

Move the negative in front of the fraction.

$9.9 = 1879.2 - \frac{319705}{171} + 215 c + 215 d - 215 c - 215 d$

$b = \frac{1487}{171} - c - d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = 1879.2 - \frac{319705}{171} + 215 c + 215 d - 215 c - 215 d$

$b = \frac{1487}{171} - c - d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.2.1.2

Combine the opposite terms in $1879.2 - \frac{319705}{171} + 215 c + 215 d - 215 c - 215 d$ .

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Step 3.3.4.2.1.2.1

Subtract $215 c$ from $215 c$ .

$9.9 = 1879.2 - \frac{319705}{171} + 215 d + 0 - 215 d$

$b = \frac{1487}{171} - c - d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.2.1.2.2

Add $1879.2 - \frac{319705}{171} + 215 d$ and $0$ .

$9.9 = 1879.2 - \frac{319705}{171} + 215 d - 215 d$

$b = \frac{1487}{171} - c - d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.2.1.2.3

Subtract $215 d$ from $215 d$ .

$9.9 = 1879.2 - \frac{319705}{171} + 0$

$b = \frac{1487}{171} - c - d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.2.1.2.4

Add $1879.2 - \frac{319705}{171}$ and $0$ .

$9.9 = 1879.2 - \frac{319705}{171}$

$b = \frac{1487}{171} - c - d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = 1879.2 - \frac{319705}{171}$

$b = \frac{1487}{171} - c - d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.2.1.3

To write $1879.2$ as a fraction with a common denominator, multiply by $\frac{171}{171}$ .

$9.9 = 1879.2 \cdot \frac{171}{171} - \frac{319705}{171}$

$b = \frac{1487}{171} - c - d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.2.1.4

Combine fractions.

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Step 3.3.4.2.1.4.1

Combine $1879.2$ and $\frac{171}{171}$ .

$9.9 = \frac{1879.2 \cdot 171}{171} - \frac{319705}{171}$

$b = \frac{1487}{171} - c - d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.2.1.4.2

Combine the numerators over the common denominator.

$9.9 = \frac{1879.2 \cdot 171 - 319705}{171}$

$b = \frac{1487}{171} - c - d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = \frac{1879.2 \cdot 171 - 319705}{171}$

$b = \frac{1487}{171} - c - d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.2.1.5

Simplify the numerator.

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Step 3.3.4.2.1.5.1

Multiply $1879.2$ by $171$ .

$9.9 = \frac{321343.2 - 319705}{171}$

$b = \frac{1487}{171} - c - d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.2.1.5.2

Subtract $319705$ from $321343.2$ .

$9.9 = \frac{1638.2}{171}$

$b = \frac{1487}{171} - c - d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = \frac{1638.2}{171}$

$b = \frac{1487}{171} - c - d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.2.1.6

Divide $1638.2$ by $171$ .

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.9 = 1087.5 - 124 b - 124 c - 124 d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.3

Replace all occurrences of $b$ in $9.9 = 1087.5 - 124 b - 124 c - 124 d$ with $\frac{1487}{171} - c - d$ .

$9.9 = 1087.5 - 124 (\frac{1487}{171} - c - d) - 124 c - 124 d$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.4

Simplify the right side.

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Step 3.3.4.4.1

Simplify $1087.5 - 124 (\frac{1487}{171} - c - d) - 124 c - 124 d$ .

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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

Apply the distributive property.

$9.9 = 1087.5 - 124 (\frac{1487}{171}) - 124 (- c) - 124 (- d) - 124 c - 124 d$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.4.1.1.2

Simplify.

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Step 3.3.4.4.1.1.2.1

Multiply $- 124 (\frac{1487}{171})$ .

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Step 3.3.4.4.1.1.2.1.1

Combine $- 124$ and $\frac{1487}{171}$ .

$9.9 = 1087.5 + \frac{- 124 \cdot 1487}{171} - 124 (- c) - 124 (- d) - 124 c - 124 d$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.4.1.1.2.1.2

Multiply $- 124$ by $1487$ .

$9.9 = 1087.5 + \frac{- 184388}{171} - 124 (- c) - 124 (- d) - 124 c - 124 d$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = 1087.5 + \frac{- 184388}{171} - 124 (- c) - 124 (- d) - 124 c - 124 d$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.4.1.1.2.2

Multiply $- 1$ by $- 124$ .

$9.9 = 1087.5 + \frac{- 184388}{171} + 124 c - 124 (- d) - 124 c - 124 d$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.4.1.1.2.3

Multiply $- 1$ by $- 124$ .

$9.9 = 1087.5 + \frac{- 184388}{171} + 124 c + 124 d - 124 c - 124 d$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = 1087.5 + \frac{- 184388}{171} + 124 c + 124 d - 124 c - 124 d$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.4.1.1.3

Move the negative in front of the fraction.

$9.9 = 1087.5 - \frac{184388}{171} + 124 c + 124 d - 124 c - 124 d$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = 1087.5 - \frac{184388}{171} + 124 c + 124 d - 124 c - 124 d$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.4.1.2

Combine the opposite terms in $1087.5 - \frac{184388}{171} + 124 c + 124 d - 124 c - 124 d$ .

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Step 3.3.4.4.1.2.1

Subtract $124 c$ from $124 c$ .

$9.9 = 1087.5 - \frac{184388}{171} + 124 d + 0 - 124 d$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.4.1.2.2

Add $1087.5 - \frac{184388}{171} + 124 d$ and $0$ .

$9.9 = 1087.5 - \frac{184388}{171} + 124 d - 124 d$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.4.1.2.3

Subtract $124 d$ from $124 d$ .

$9.9 = 1087.5 - \frac{184388}{171} + 0$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.4.1.2.4

Add $1087.5 - \frac{184388}{171}$ and $0$ .

$9.9 = 1087.5 - \frac{184388}{171}$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = 1087.5 - \frac{184388}{171}$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.4.1.3

To write $1087.5$ as a fraction with a common denominator, multiply by $\frac{171}{171}$ .

$9.9 = 1087.5 \cdot \frac{171}{171} - \frac{184388}{171}$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.4.1.4

Combine fractions.

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Step 3.3.4.4.1.4.1

Combine $1087.5$ and $\frac{171}{171}$ .

$9.9 = \frac{1087.5 \cdot 171}{171} - \frac{184388}{171}$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.4.1.4.2

Combine the numerators over the common denominator.

$9.9 = \frac{1087.5 \cdot 171 - 184388}{171}$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = \frac{1087.5 \cdot 171 - 184388}{171}$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.4.1.5

Simplify the numerator.

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Step 3.3.4.4.1.5.1

Multiply $1087.5$ by $171$ .

$9.9 = \frac{185962.5 - 184388}{171}$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.4.1.5.2

Subtract $184388$ from $185962.5$ .

$9.9 = \frac{1574.5}{171}$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = \frac{1574.5}{171}$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.4.1.6

Divide $1574.5$ by $171$ .

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.5 = 556.8 - 63 b - 63 c - 63 d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.5

Replace all occurrences of $b$ in $9.5 = 556.8 - 63 b - 63 c - 63 d$ with $\frac{1487}{171} - c - d$ .

$9.5 = 556.8 - 63 (\frac{1487}{171} - c - d) - 63 c - 63 d$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.6

Simplify the right side.

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Step 3.3.4.6.1

Simplify $556.8 - 63 (\frac{1487}{171} - c - d) - 63 c - 63 d$ .

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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

Apply the distributive property.

$9.5 = 556.8 - 63 (\frac{1487}{171}) - 63 (- c) - 63 (- d) - 63 c - 63 d$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.6.1.1.2

Simplify.

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Step 3.3.4.6.1.1.2.1

Cancel the common factor of $9$ .

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Step 3.3.4.6.1.1.2.1.1

Factor $9$ out of $- 63$ .

$9.5 = 556.8 + 9 (- 7) (\frac{1487}{171}) - 63 (- c) - 63 (- d) - 63 c - 63 d$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.6.1.1.2.1.2

Factor $9$ out of $171$ .

$9.5 = 556.8 + 9 \cdot (- 7 \frac{1487}{9 \cdot 19}) - 63 (- c) - 63 (- d) - 63 c - 63 d$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.6.1.1.2.1.3

Cancel the common factor.

$9.5 = 556.8 + 9 \cdot (- 7 \frac{1487}{9 \cdot 19}) - 63 (- c) - 63 (- d) - 63 c - 63 d$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.6.1.1.2.1.4

Rewrite the expression.

$9.5 = 556.8 - 7 (\frac{1487}{19}) - 63 (- c) - 63 (- d) - 63 c - 63 d$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.5 = 556.8 - 7 (\frac{1487}{19}) - 63 (- c) - 63 (- d) - 63 c - 63 d$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.6.1.1.2.2

Combine $- 7$ and $\frac{1487}{19}$ .

$9.5 = 556.8 + \frac{- 7 \cdot 1487}{19} - 63 (- c) - 63 (- d) - 63 c - 63 d$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.6.1.1.2.3

Multiply $- 7$ by $1487$ .

$9.5 = 556.8 + \frac{- 10409}{19} - 63 (- c) - 63 (- d) - 63 c - 63 d$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.6.1.1.2.4

Multiply $- 1$ by $- 63$ .

$9.5 = 556.8 + \frac{- 10409}{19} + 63 c - 63 (- d) - 63 c - 63 d$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.6.1.1.2.5

Multiply $- 1$ by $- 63$ .

$9.5 = 556.8 + \frac{- 10409}{19} + 63 c + 63 d - 63 c - 63 d$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.5 = 556.8 + \frac{- 10409}{19} + 63 c + 63 d - 63 c - 63 d$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.6.1.1.3

Move the negative in front of the fraction.

$9.5 = 556.8 - \frac{10409}{19} + 63 c + 63 d - 63 c - 63 d$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.5 = 556.8 - \frac{10409}{19} + 63 c + 63 d - 63 c - 63 d$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.6.1.2

Combine the opposite terms in $556.8 - \frac{10409}{19} + 63 c + 63 d - 63 c - 63 d$ .

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Step 3.3.4.6.1.2.1

Subtract $63 c$ from $63 c$ .

$9.5 = 556.8 - \frac{10409}{19} + 63 d + 0 - 63 d$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.6.1.2.2

Add $556.8 - \frac{10409}{19} + 63 d$ and $0$ .

$9.5 = 556.8 - \frac{10409}{19} + 63 d - 63 d$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.6.1.2.3

Subtract $63 d$ from $63 d$ .

$9.5 = 556.8 - \frac{10409}{19} + 0$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.6.1.2.4

Add $556.8 - \frac{10409}{19}$ and $0$ .

$9.5 = 556.8 - \frac{10409}{19}$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.5 = 556.8 - \frac{10409}{19}$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.6.1.3

To write $556.8$ as a fraction with a common denominator, multiply by $\frac{19}{19}$ .

$9.5 = 556.8 \cdot \frac{19}{19} - \frac{10409}{19}$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.6.1.4

Combine fractions.

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Step 3.3.4.6.1.4.1

Combine $556.8$ and $\frac{19}{19}$ .

$9.5 = \frac{556.8 \cdot 19}{19} - \frac{10409}{19}$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.6.1.4.2

Combine the numerators over the common denominator.

$9.5 = \frac{556.8 \cdot 19 - 10409}{19}$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.5 = \frac{556.8 \cdot 19 - 10409}{19}$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.6.1.5

Simplify the numerator.

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Step 3.3.4.6.1.5.1

Multiply $556.8$ by $19$ .

$9.5 = \frac{10579.2 - 10409}{19}$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.6.1.5.2

Subtract $10409$ from $10579.2$ .

$9.5 = \frac{170.2}{19}$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.5 = \frac{170.2}{19}$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.6.1.6

Divide $170.2$ by $19$ .

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$9.2 = 234.9 - 26 b - 26 c - 26 d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.7

Replace all occurrences of $b$ in $9.2 = 234.9 - 26 b - 26 c - 26 d$ with $\frac{1487}{171} - c - d$ .

$9.2 = 234.9 - 26 (\frac{1487}{171} - c - d) - 26 c - 26 d$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.8

Simplify the right side.

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Step 3.3.4.8.1

Simplify $234.9 - 26 (\frac{1487}{171} - c - d) - 26 c - 26 d$ .

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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

Apply the distributive property.

$9.2 = 234.9 - 26 (\frac{1487}{171}) - 26 (- c) - 26 (- d) - 26 c - 26 d$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.8.1.1.2

Simplify.

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Step 3.3.4.8.1.1.2.1

Multiply $- 26 (\frac{1487}{171})$ .

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Step 3.3.4.8.1.1.2.1.1

Combine $- 26$ and $\frac{1487}{171}$ .

$9.2 = 234.9 + \frac{- 26 \cdot 1487}{171} - 26 (- c) - 26 (- d) - 26 c - 26 d$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.8.1.1.2.1.2

Multiply $- 26$ by $1487$ .

$9.2 = 234.9 + \frac{- 38662}{171} - 26 (- c) - 26 (- d) - 26 c - 26 d$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.2 = 234.9 + \frac{- 38662}{171} - 26 (- c) - 26 (- d) - 26 c - 26 d$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.8.1.1.2.2

Multiply $- 1$ by $- 26$ .

$9.2 = 234.9 + \frac{- 38662}{171} + 26 c - 26 (- d) - 26 c - 26 d$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.8.1.1.2.3

Multiply $- 1$ by $- 26$ .

$9.2 = 234.9 + \frac{- 38662}{171} + 26 c + 26 d - 26 c - 26 d$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.2 = 234.9 + \frac{- 38662}{171} + 26 c + 26 d - 26 c - 26 d$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.8.1.1.3

Move the negative in front of the fraction.

$9.2 = 234.9 - \frac{38662}{171} + 26 c + 26 d - 26 c - 26 d$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.2 = 234.9 - \frac{38662}{171} + 26 c + 26 d - 26 c - 26 d$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.8.1.2

Combine the opposite terms in $234.9 - \frac{38662}{171} + 26 c + 26 d - 26 c - 26 d$ .

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Step 3.3.4.8.1.2.1

Subtract $26 c$ from $26 c$ .

$9.2 = 234.9 - \frac{38662}{171} + 26 d + 0 - 26 d$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.8.1.2.2

Add $234.9 - \frac{38662}{171} + 26 d$ and $0$ .

$9.2 = 234.9 - \frac{38662}{171} + 26 d - 26 d$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.8.1.2.3

Subtract $26 d$ from $26 d$ .

$9.2 = 234.9 - \frac{38662}{171} + 0$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.8.1.2.4

Add $234.9 - \frac{38662}{171}$ and $0$ .

$9.2 = 234.9 - \frac{38662}{171}$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.2 = 234.9 - \frac{38662}{171}$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.8.1.3

To write $234.9$ as a fraction with a common denominator, multiply by $\frac{171}{171}$ .

$9.2 = 234.9 \cdot \frac{171}{171} - \frac{38662}{171}$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.8.1.4

Combine fractions.

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Step 3.3.4.8.1.4.1

Combine $234.9$ and $\frac{171}{171}$ .

$9.2 = \frac{234.9 \cdot 171}{171} - \frac{38662}{171}$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.8.1.4.2

Combine the numerators over the common denominator.

$9.2 = \frac{234.9 \cdot 171 - 38662}{171}$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.2 = \frac{234.9 \cdot 171 - 38662}{171}$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.8.1.5

Simplify the numerator.

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Step 3.3.4.8.1.5.1

Multiply $234.9$ by $171$ .

$9.2 = \frac{40167.9 - 38662}{171}$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.8.1.5.2

Subtract $38662$ from $40167.9$ .

$9.2 = \frac{1505.9}{171}$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.2 = \frac{1505.9}{171}$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.8.1.6

Divide $1505.9$ by $171$ .

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$8.7 = 69.6 - 7 b - 7 c - 7 d$

$a = 8.7 - b - c - d$

Step 3.3.4.9

Replace all occurrences of $b$ in $8.7 = 69.6 - 7 b - 7 c - 7 d$ with $\frac{1487}{171} - c - d$ .

$8.7 = 69.6 - 7 (\frac{1487}{171} - c - d) - 7 c - 7 d$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - b - c - d$

Step 3.3.4.10

Simplify the right side.

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Step 3.3.4.10.1

Simplify $69.6 - 7 (\frac{1487}{171} - c - d) - 7 c - 7 d$ .

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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

Apply the distributive property.

$8.7 = 69.6 - 7 (\frac{1487}{171}) - 7 (- c) - 7 (- d) - 7 c - 7 d$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - b - c - d$

Step 3.3.4.10.1.1.2

Simplify.

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Step 3.3.4.10.1.1.2.1

Multiply $- 7 (\frac{1487}{171})$ .

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Step 3.3.4.10.1.1.2.1.1

Combine $- 7$ and $\frac{1487}{171}$ .

$8.7 = 69.6 + \frac{- 7 \cdot 1487}{171} - 7 (- c) - 7 (- d) - 7 c - 7 d$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - b - c - d$

Step 3.3.4.10.1.1.2.1.2

Multiply $- 7$ by $1487$ .

$8.7 = 69.6 + \frac{- 10409}{171} - 7 (- c) - 7 (- d) - 7 c - 7 d$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - b - c - d$

$8.7 = 69.6 + \frac{- 10409}{171} - 7 (- c) - 7 (- d) - 7 c - 7 d$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - b - c - d$

Step 3.3.4.10.1.1.2.2

Multiply $- 1$ by $- 7$ .

$8.7 = 69.6 + \frac{- 10409}{171} + 7 c - 7 (- d) - 7 c - 7 d$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - b - c - d$

Step 3.3.4.10.1.1.2.3

Multiply $- 1$ by $- 7$ .

$8.7 = 69.6 + \frac{- 10409}{171} + 7 c + 7 d - 7 c - 7 d$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - b - c - d$

$8.7 = 69.6 + \frac{- 10409}{171} + 7 c + 7 d - 7 c - 7 d$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - b - c - d$

Step 3.3.4.10.1.1.3

Move the negative in front of the fraction.

$8.7 = 69.6 - \frac{10409}{171} + 7 c + 7 d - 7 c - 7 d$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - b - c - d$

$8.7 = 69.6 - \frac{10409}{171} + 7 c + 7 d - 7 c - 7 d$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - b - c - d$

Step 3.3.4.10.1.2

Combine the opposite terms in $69.6 - \frac{10409}{171} + 7 c + 7 d - 7 c - 7 d$ .

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Step 3.3.4.10.1.2.1

Subtract $7 c$ from $7 c$ .

$8.7 = 69.6 - \frac{10409}{171} + 7 d + 0 - 7 d$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - b - c - d$

Step 3.3.4.10.1.2.2

Add $69.6 - \frac{10409}{171} + 7 d$ and $0$ .

$8.7 = 69.6 - \frac{10409}{171} + 7 d - 7 d$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - b - c - d$

Step 3.3.4.10.1.2.3

Subtract $7 d$ from $7 d$ .

$8.7 = 69.6 - \frac{10409}{171} + 0$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - b - c - d$

Step 3.3.4.10.1.2.4

Add $69.6 - \frac{10409}{171}$ and $0$ .

$8.7 = 69.6 - \frac{10409}{171}$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - b - c - d$

$8.7 = 69.6 - \frac{10409}{171}$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - b - c - d$

Step 3.3.4.10.1.3

To write $69.6$ as a fraction with a common denominator, multiply by $\frac{171}{171}$ .

$8.7 = 69.6 \cdot \frac{171}{171} - \frac{10409}{171}$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - b - c - d$

Step 3.3.4.10.1.4

Combine fractions.

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Step 3.3.4.10.1.4.1

Combine $69.6$ and $\frac{171}{171}$ .

$8.7 = \frac{69.6 \cdot 171}{171} - \frac{10409}{171}$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - b - c - d$

Step 3.3.4.10.1.4.2

Combine the numerators over the common denominator.

$8.7 = \frac{69.6 \cdot 171 - 10409}{171}$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - b - c - d$

$8.7 = \frac{69.6 \cdot 171 - 10409}{171}$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - b - c - d$

Step 3.3.4.10.1.5

Simplify the numerator.

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Step 3.3.4.10.1.5.1

Multiply $69.6$ by $171$ .

$8.7 = \frac{11901.6 - 10409}{171}$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - b - c - d$

Step 3.3.4.10.1.5.2

Subtract $10409$ from $11901.6$ .

$8.7 = \frac{1492.6}{171}$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - b - c - d$

$8.7 = \frac{1492.6}{171}$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - b - c - d$

Step 3.3.4.10.1.6

Divide $1492.6$ by $171$ .

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - b - c - d$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - b - c - d$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - b - c - d$

Step 3.3.4.11

Replace all occurrences of $b$ in $a = 8.7 - b - c - d$ with $\frac{1487}{171} - c - d$ .

$a = 8.7 - (\frac{1487}{171} - c - d) - c - d$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

Step 3.3.4.12

Simplify the right side.

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Step 3.3.4.12.1

Simplify $8.7 - (\frac{1487}{171} - c - d) - c - d$ .

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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

Apply the distributive property.

$a = 8.7 - \frac{1487}{171} + c + d - c - d$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

Step 3.3.4.12.1.1.2

Simplify.

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Step 3.3.4.12.1.1.2.1

Multiply $- - c$ .

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Step 3.3.4.12.1.1.2.1.1

Multiply $- 1$ by $- 1$ .

$a = 8.7 - \frac{1487}{171} + 1 c + d - c - d$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

Step 3.3.4.12.1.1.2.1.2

Multiply $c$ by $1$ .

$a = 8.7 - \frac{1487}{171} + c + d - c - d$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - \frac{1487}{171} + c + d - c - d$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

Step 3.3.4.12.1.1.2.2

Multiply $- - d$ .

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Step 3.3.4.12.1.1.2.2.1

Multiply $- 1$ by $- 1$ .

$a = 8.7 - \frac{1487}{171} + c + 1 d - c - d$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

Step 3.3.4.12.1.1.2.2.2

Multiply $d$ by $1$ .

$a = 8.7 - \frac{1487}{171} + c + d - c - d$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - \frac{1487}{171} + c + d - c - d$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - \frac{1487}{171} + c + d - c - d$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - \frac{1487}{171} + c + d - c - d$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

Step 3.3.4.12.1.2

Combine the opposite terms in $8.7 - \frac{1487}{171} + c + d - c - d$ .

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Step 3.3.4.12.1.2.1

Subtract $c$ from $c$ .

$a = 8.7 - \frac{1487}{171} + d + 0 - d$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

Step 3.3.4.12.1.2.2

Add $8.7 - \frac{1487}{171} + d$ and $0$ .

$a = 8.7 - \frac{1487}{171} + d - d$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

Step 3.3.4.12.1.2.3

Subtract $d$ from $d$ .

$a = 8.7 - \frac{1487}{171} + 0$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

Step 3.3.4.12.1.2.4

Add $8.7 - \frac{1487}{171}$ and $0$ .

$a = 8.7 - \frac{1487}{171}$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 8.7 - \frac{1487}{171}$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

Step 3.3.4.12.1.3

To write $8.7$ as a fraction with a common denominator, multiply by $\frac{171}{171}$ .

$a = 8.7 \cdot \frac{171}{171} - \frac{1487}{171}$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

Step 3.3.4.12.1.4

Combine fractions.

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Step 3.3.4.12.1.4.1

Combine $8.7$ and $\frac{171}{171}$ .

$a = \frac{8.7 \cdot 171}{171} - \frac{1487}{171}$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

Step 3.3.4.12.1.4.2

Combine the numerators over the common denominator.

$a = \frac{8.7 \cdot 171 - 1487}{171}$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = \frac{8.7 \cdot 171 - 1487}{171}$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

Step 3.3.4.12.1.5

Simplify the numerator.

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Step 3.3.4.12.1.5.1

Multiply $8.7$ by $171$ .

$a = \frac{1487.7 - 1487}{171}$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

Step 3.3.4.12.1.5.2

Subtract $1487$ from $1487.7$ .

$a = \frac{0.7}{171}$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = \frac{0.7}{171}$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

Step 3.3.4.12.1.6

Divide $0.7$ by $171$ .

$a = 0.00409356$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 0.00409356$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 0.00409356$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

$a = 0.00409356$

$8.7 = 8.72865497$

$9.2 = 8.80643274$

$9.5 = 8.95789473$

$9.9 = 9.20760233$

$9.9 = 9.58011695$

$b = \frac{1487}{171} - c - d$

Step 3.3.5

Since $8.7 = 8.72865497$ 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 $x = 1$ .

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Step 3.4.1.1

Simplify each term.

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Step 3.4.1.1.1

One to any power is one.

$y = 0 \cdot 1 + (0) \cdot (1^{2}) + (0) \cdot ((1) \cdot 0)$

Step 3.4.1.1.2

Multiply $0$ by $1$ .

$y = 0 + (0) \cdot (1^{2}) + (0) \cdot ((1) \cdot 0)$

Step 3.4.1.1.3

One to any power is one.

$y = 0 + 0 \cdot 1 + (0) \cdot ((1) \cdot 0)$

Step 3.4.1.1.4

Multiply $0$ by $1$ .

$y = 0 + 0 + (0) \cdot ((1) \cdot 0)$

Step 3.4.1.1.5

Multiply $(0) ((1) \cdot 0)$ .

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Step 3.4.1.1.5.1

Multiply $0$ by $1$ .

$y = 0 + 0 + 0 \cdot 0$

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, $x = 1$ . This check does not pass, since $y = 0$ and $y = 8.7$ . The function rule can't be cubic.

$0 \neq 8.7$

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.