Basic Math Examples

$- 7 = \frac{5 y - 12}{- 4}$

Step 1

Rewrite the equation as $\frac{5 y - 12}{- 4} = - 7$ .

$\frac{5 y - 12}{- 4} = - 7$

Step 2

Multiply both sides by $- 4$ .

$\frac{5 y - 12}{- 4} \cdot - 4 = - 7 \cdot - 4$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{5 y - 12}{- 4} \cdot - 4$ .

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Step 3.1.1.1

Cancel the common factor of $4$ .

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Step 3.1.1.1.1

Factor $4$ out of $- 4$ .

$\frac{5 y - 12}{4 (- 1)} \cdot - 4 = - 7 \cdot - 4$

Step 3.1.1.1.2

Factor $4$ out of $- 4$ .

$\frac{5 y - 12}{4 \cdot - 1} \cdot (4 \cdot - 1) = - 7 \cdot - 4$

Step 3.1.1.1.3

Cancel the common factor.

$\frac{5 y - 12}{4 \cdot - 1} \cdot (4 \cdot - 1) = - 7 \cdot - 4$

Step 3.1.1.1.4

Rewrite the expression.

$\frac{5 y - 12}{- 1} \cdot - 1 = - 7 \cdot - 4$

Step 3.1.1.2

Combine $\frac{5 y - 12}{- 1}$ and $- 1$ .

$\frac{(5 y - 12) \cdot - 1}{- 1} = - 7 \cdot - 4$

Step 3.1.1.3

Simplify the expression.

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Step 3.1.1.3.1

Move the negative one from the denominator of $\frac{(5 y - 12) \cdot - 1}{- 1}$ .

$- 1 \cdot ((5 y - 12) \cdot - 1) = - 7 \cdot - 4$

Step 3.1.1.3.2

Rewrite $- 1 \cdot ((5 y - 12) \cdot - 1)$ as $- ((5 y - 12) \cdot - 1)$ .

$- ((5 y - 12) \cdot - 1) = - 7 \cdot - 4$

Step 3.1.1.4

Apply the distributive property.

$- (5 y \cdot - 1 - 12 \cdot - 1) = - 7 \cdot - 4$

Step 3.1.1.5

Multiply.

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Step 3.1.1.5.1

Multiply $- 1$ by $5$ .

$- (- 5 y - 12 \cdot - 1) = - 7 \cdot - 4$

Step 3.1.1.5.2

Multiply $- 12$ by $- 1$ .

$- (- 5 y + 12) = - 7 \cdot - 4$

Step 3.1.1.6

Apply the distributive property.

$- (- 5 y) - 1 \cdot 12 = - 7 \cdot - 4$

Step 3.1.1.7

Multiply.

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Step 3.1.1.7.1

Multiply $- 5$ by $- 1$ .

$5 y - 1 \cdot 12 = - 7 \cdot - 4$

Step 3.1.1.7.2

Multiply $- 1$ by $12$ .

$5 y - 12 = - 7 \cdot - 4$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $- 7$ by $- 4$ .

$5 y - 12 = 28$

Step 4

Solve for $y$ .

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Step 4.1

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

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Step 4.1.1

Add $12$ to both sides of the equation.

$5 y = 28 + 12$

Step 4.1.2

Add $28$ and $12$ .

$5 y = 40$

Step 4.2

Divide each term in $5 y = 40$ by $5$ and simplify.

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Step 4.2.1

Divide each term in $5 y = 40$ by $5$ .

$\frac{5 y}{5} = \frac{40}{5}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $5$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{40}{5}$

Step 4.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{40}{5}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $40$ by $5$ .

$y = 8$