Basic Math Examples

$11 - (30 - 8 \div (5 - y \div 9) \cdot 7) = 9$

Step 1

Simplify $11 - (30 - 8 \div (5 - y \div 9) \cdot 7)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Simplify the denominator.

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Step 1.1.1.1.1

Rewrite the division as a fraction.

$11 - (30 - 8 \div (5 - \frac{y}{9}) \cdot 7) = 9$

Step 1.1.1.1.2

To write $5$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$11 - (30 - 8 \div (5 \cdot \frac{9}{9} - \frac{y}{9}) \cdot 7) = 9$

Step 1.1.1.1.3

Combine $5$ and $\frac{9}{9}$ .

$11 - (30 - 8 \div (\frac{5 \cdot 9}{9} - \frac{y}{9}) \cdot 7) = 9$

Step 1.1.1.1.4

Combine the numerators over the common denominator.

$11 - (30 - 8 \div \frac{5 \cdot 9 - y}{9} \cdot 7) = 9$

Step 1.1.1.1.5

Multiply $5$ by $9$ .

$11 - (30 - 8 \div \frac{45 - y}{9} \cdot 7) = 9$

Step 1.1.1.2

To divide by a fraction, multiply by its reciprocal.

$11 - (30 - (8 \frac{9}{45 - y}) \cdot 7) = 9$

Step 1.1.1.3

Multiply $8 \frac{9}{45 - y}$ .

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Step 1.1.1.3.1

Combine $8$ and $\frac{9}{45 - y}$ .

$11 - (30 - \frac{8 \cdot 9}{45 - y} \cdot 7) = 9$

Step 1.1.1.3.2

Multiply $8$ by $9$ .

$11 - (30 - \frac{72}{45 - y} \cdot 7) = 9$

Step 1.1.1.4

Multiply $- \frac{72}{45 - y} \cdot 7$ .

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Step 1.1.1.4.1

Multiply $7$ by $- 1$ .

$11 - (30 - 7 \frac{72}{45 - y}) = 9$

Step 1.1.1.4.2

Combine $- 7$ and $\frac{72}{45 - y}$ .

$11 - (30 + \frac{- 7 \cdot 72}{45 - y}) = 9$

Step 1.1.1.4.3

Multiply $- 7$ by $72$ .

$11 - (30 + \frac{- 504}{45 - y}) = 9$

Step 1.1.1.5

Move the negative in front of the fraction.

$11 - (30 - \frac{504}{45 - y}) = 9$

Step 1.1.2

To write $30$ as a fraction with a common denominator, multiply by $\frac{45 - y}{45 - y}$ .

$11 - (\frac{30 (45 - y)}{45 - y} - \frac{504}{45 - y}) = 9$

Step 1.1.3

Combine the numerators over the common denominator.

$11 - \frac{30 (45 - y) - 504}{45 - y} = 9$

Step 1.1.4

Simplify the numerator.

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Step 1.1.4.1

Factor $6$ out of $30 (45 - y) - 504$ .

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Step 1.1.4.1.1

Factor $6$ out of $30 (45 - y)$ .

$11 - \frac{6 (5 (45 - y)) - 504}{45 - y} = 9$

Step 1.1.4.1.2

Factor $6$ out of $- 504$ .

$11 - \frac{6 (5 (45 - y)) + 6 (- 84)}{45 - y} = 9$

Step 1.1.4.1.3

Factor $6$ out of $6 (5 (45 - y)) + 6 (- 84)$ .

$11 - \frac{6 (5 (45 - y) - 84)}{45 - y} = 9$

Step 1.1.4.2

Apply the distributive property.

$11 - \frac{6 (5 \cdot 45 + 5 (- y) - 84)}{45 - y} = 9$

Step 1.1.4.3

Multiply $5$ by $45$ .

$11 - \frac{6 (225 + 5 (- y) - 84)}{45 - y} = 9$

Step 1.1.4.4

Multiply $- 1$ by $5$ .

$11 - \frac{6 (225 - 5 y - 84)}{45 - y} = 9$

Step 1.1.4.5

Subtract $84$ from $225$ .

$11 - \frac{6 (- 5 y + 141)}{45 - y} = 9$

Step 1.2

To write $11$ as a fraction with a common denominator, multiply by $\frac{45 - y}{45 - y}$ .

$\frac{11 (45 - y)}{45 - y} - \frac{6 (- 5 y + 141)}{45 - y} = 9$

Step 1.3

Combine the numerators over the common denominator.

$\frac{11 (45 - y) - 6 (- 5 y + 141)}{45 - y} = 9$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Apply the distributive property.

$\frac{11 \cdot 45 + 11 (- y) - 6 (- 5 y + 141)}{45 - y} = 9$

Step 1.4.2

Multiply $11$ by $45$ .

$\frac{495 + 11 (- y) - 6 (- 5 y + 141)}{45 - y} = 9$

Step 1.4.3

Multiply $- 1$ by $11$ .

$\frac{495 - 11 y - 6 (- 5 y + 141)}{45 - y} = 9$

Step 1.4.4

Apply the distributive property.

$\frac{495 - 11 y - 6 (- 5 y) - 6 \cdot 141}{45 - y} = 9$

Step 1.4.5

Multiply $- 5$ by $- 6$ .

$\frac{495 - 11 y + 30 y - 6 \cdot 141}{45 - y} = 9$

Step 1.4.6

Multiply $- 6$ by $141$ .

$\frac{495 - 11 y + 30 y - 846}{45 - y} = 9$

Step 1.4.7

Subtract $846$ from $495$ .

$\frac{- 11 y + 30 y - 351}{45 - y} = 9$

Step 1.4.8

Add $- 11 y$ and $30 y$ .

$\frac{19 y - 351}{45 - y} = 9$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$45 - y, 1$

Step 2.2

Remove parentheses.

$45 - y, 1$

Step 2.3

The LCM of one and any expression is the expression.

$45 - y$

Step 3

Multiply each term in $\frac{19 y - 351}{45 - y} = 9$ by $45 - y$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{19 y - 351}{45 - y} = 9$ by $45 - y$ .

$\frac{19 y - 351}{45 - y} (45 - y) = 9 (45 - y)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $45 - y$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{19 y - 351}{45 - y} (45 - y) = 9 (45 - y)$

Step 3.2.1.2

Rewrite the expression.

$19 y - 351 = 9 (45 - y)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$19 y - 351 = 9 \cdot 45 + 9 (- y)$

Step 3.3.2

Multiply.

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Step 3.3.2.1

Multiply $9$ by $45$ .

$19 y - 351 = 405 + 9 (- y)$

Step 3.3.2.2

Multiply $- 1$ by $9$ .

$19 y - 351 = 405 - 9 y$

Step 4

Solve the equation.

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Step 4.1

Move all terms containing $y$ to the left side of the equation.

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Step 4.1.1

Add $9 y$ to both sides of the equation.

$19 y - 351 + 9 y = 405$

Step 4.1.2

Add $19 y$ and $9 y$ .

$28 y - 351 = 405$

Step 4.2

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

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Step 4.2.1

Add $351$ to both sides of the equation.

$28 y = 405 + 351$

Step 4.2.2

Add $405$ and $351$ .

$28 y = 756$

Step 4.3

Divide each term in $28 y = 756$ by $28$ and simplify.

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Step 4.3.1

Divide each term in $28 y = 756$ by $28$ .

$\frac{28 y}{28} = \frac{756}{28}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $28$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{28 y}{28} = \frac{756}{28}$

Step 4.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{756}{28}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $756$ by $28$ .

$y = 27$