Basic Math Examples

$\frac{y + 1}{4} = 12 - \frac{8 y - 6}{5}$

Step 1

Multiply both sides by $4$ .

$\frac{y + 1}{4} \cdot 4 = (12 - \frac{8 y - 6}{5}) \cdot 4$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $4$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{y + 1}{4} \cdot 4 = (12 - \frac{8 y - 6}{5}) \cdot 4$

Step 2.1.1.2

Rewrite the expression.

$y + 1 = (12 - \frac{8 y - 6}{5}) \cdot 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(12 - \frac{8 y - 6}{5}) \cdot 4$ .

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Step 2.2.1.1

Factor $2$ out of $8 y - 6$ .

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Step 2.2.1.1.1

Factor $2$ out of $8 y$ .

$y + 1 = (12 - \frac{2 (4 y) - 6}{5}) \cdot 4$

Step 2.2.1.1.2

Factor $2$ out of $- 6$ .

$y + 1 = (12 - \frac{2 (4 y) + 2 (- 3)}{5}) \cdot 4$

Step 2.2.1.1.3

Factor $2$ out of $2 (4 y) + 2 (- 3)$ .

$y + 1 = (12 - \frac{2 (4 y - 3)}{5}) \cdot 4$

Step 2.2.1.2

To write $12$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y + 1 = (12 \cdot \frac{5}{5} - \frac{2 (4 y - 3)}{5}) \cdot 4$

Step 2.2.1.3

Simplify terms.

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Step 2.2.1.3.1

Combine $12$ and $\frac{5}{5}$ .

$y + 1 = (\frac{12 \cdot 5}{5} - \frac{2 (4 y - 3)}{5}) \cdot 4$

Step 2.2.1.3.2

Combine the numerators over the common denominator.

$y + 1 = \frac{12 \cdot 5 - 2 (4 y - 3)}{5} \cdot 4$

Step 2.2.1.4

Simplify the numerator.

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Step 2.2.1.4.1

Factor $2$ out of $12 \cdot 5 - 2 (4 y - 3)$ .

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Step 2.2.1.4.1.1

Factor $2$ out of $12 \cdot 5$ .

$y + 1 = \frac{2 (6 \cdot 5) - 2 (4 y - 3)}{5} \cdot 4$

Step 2.2.1.4.1.2

Factor $2$ out of $- 2 (4 y - 3)$ .

$y + 1 = \frac{2 (6 \cdot 5) + 2 (- (4 y - 3))}{5} \cdot 4$

Step 2.2.1.4.1.3

Factor $2$ out of $2 (6 \cdot 5) + 2 (- (4 y - 3))$ .

$y + 1 = \frac{2 (6 \cdot 5 - (4 y - 3))}{5} \cdot 4$

Step 2.2.1.4.2

Multiply $6$ by $5$ .

$y + 1 = \frac{2 (30 - (4 y - 3))}{5} \cdot 4$

Step 2.2.1.4.3

Apply the distributive property.

$y + 1 = \frac{2 (30 - (4 y) - - 3)}{5} \cdot 4$

Step 2.2.1.4.4

Multiply $4$ by $- 1$ .

$y + 1 = \frac{2 (30 - 4 y - - 3)}{5} \cdot 4$

Step 2.2.1.4.5

Multiply $- 1$ by $- 3$ .

$y + 1 = \frac{2 (30 - 4 y + 3)}{5} \cdot 4$

Step 2.2.1.4.6

Add $30$ and $3$ .

$y + 1 = \frac{2 (- 4 y + 33)}{5} \cdot 4$

Step 2.2.1.5

Multiply $\frac{2 (- 4 y + 33)}{5} \cdot 4$ .

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Step 2.2.1.5.1

Combine $\frac{2 (- 4 y + 33)}{5}$ and $4$ .

$y + 1 = \frac{2 (- 4 y + 33) \cdot 4}{5}$

Step 2.2.1.5.2

Multiply $4$ by $2$ .

$y + 1 = \frac{8 (- 4 y + 33)}{5}$

Step 2.2.1.6

Factor $- 1$ out of $- 4 y$ .

$y + 1 = \frac{8 (- (4 y) + 33)}{5}$

Step 2.2.1.7

Rewrite $33$ as $- 1 (- 33)$ .

$y + 1 = \frac{8 (- (4 y) - 1 (- 33))}{5}$

Step 2.2.1.8

Factor $- 1$ out of $- (4 y) - 1 (- 33)$ .

$y + 1 = \frac{8 (- (4 y - 33))}{5}$

Step 2.2.1.9

Simplify the expression.

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Step 2.2.1.9.1

Rewrite $- (4 y - 33)$ as $- 1 (4 y - 33)$ .

$y + 1 = \frac{8 (- 1 (4 y - 33))}{5}$

Step 2.2.1.9.2

Move the negative in front of the fraction.

$y + 1 = - \frac{8 (4 y - 33)}{5}$

Step 3

Solve for $y$ .

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Step 3.1

Multiply both sides by $5$ .

$(y + 1) \cdot 5 = - \frac{8 (4 y - 33)}{5} \cdot 5$

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Simplify $(y + 1) \cdot 5$ .

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Step 3.2.1.1.1

Apply the distributive property.

$y \cdot 5 + 1 \cdot 5 = - \frac{8 (4 y - 33)}{5} \cdot 5$

Step 3.2.1.1.2

Simplify the expression.

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Step 3.2.1.1.2.1

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

$5 \cdot y + 1 \cdot 5 = - \frac{8 (4 y - 33)}{5} \cdot 5$

Step 3.2.1.1.2.2

Multiply $5$ by $1$ .

$5 y + 5 = - \frac{8 (4 y - 33)}{5} \cdot 5$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $- \frac{8 (4 y - 33)}{5} \cdot 5$ .

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Step 3.2.2.1.1

Cancel the common factor of $5$ .

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Step 3.2.2.1.1.1

Move the leading negative in $- \frac{8 (4 y - 33)}{5}$ into the numerator.

$5 y + 5 = \frac{- 8 (4 y - 33)}{5} \cdot 5$

Step 3.2.2.1.1.2

Cancel the common factor.

$5 y + 5 = \frac{- 8 (4 y - 33)}{5} \cdot 5$

Step 3.2.2.1.1.3

Rewrite the expression.

$5 y + 5 = - 8 (4 y - 33)$

Step 3.2.2.1.2

Apply the distributive property.

$5 y + 5 = - 8 (4 y) - 8 \cdot - 33$

Step 3.2.2.1.3

Multiply.

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Step 3.2.2.1.3.1

Multiply $4$ by $- 8$ .

$5 y + 5 = - 32 y - 8 \cdot - 33$

Step 3.2.2.1.3.2

Multiply $- 8$ by $- 33$ .

$5 y + 5 = - 32 y + 264$

Step 3.3

Solve for $y$ .

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Step 3.3.1

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

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Step 3.3.1.1

Add $32 y$ to both sides of the equation.

$5 y + 5 + 32 y = 264$

Step 3.3.1.2

Add $5 y$ and $32 y$ .

$37 y + 5 = 264$

Step 3.3.2

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

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Step 3.3.2.1

Subtract $5$ from both sides of the equation.

$37 y = 264 - 5$

Step 3.3.2.2

Subtract $5$ from $264$ .

$37 y = 259$

Step 3.3.3

Divide each term in $37 y = 259$ by $37$ and simplify.

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Step 3.3.3.1

Divide each term in $37 y = 259$ by $37$ .

$\frac{37 y}{37} = \frac{259}{37}$

Step 3.3.3.2

Simplify the left side.

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Step 3.3.3.2.1

Cancel the common factor of $37$ .

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Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{37 y}{37} = \frac{259}{37}$

Step 3.3.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{259}{37}$

Step 3.3.3.3

Simplify the right side.

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Step 3.3.3.3.1

Divide $259$ by $37$ .

$y = 7$