Pre-Algebra Examples

$- \frac{3}{7} y = 12$

Step 1

Multiply both sides of the equation by $- \frac{7}{3}$ .

$- \frac{7}{3} (- \frac{3}{7} y) = - \frac{7}{3} \cdot 12$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $- \frac{7}{3} (- \frac{3}{7} y)$ .

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Step 2.1.1.1

Combine $y$ and $\frac{3}{7}$ .

$- \frac{7}{3} (- \frac{y \cdot 3}{7}) = - \frac{7}{3} \cdot 12$

Step 2.1.1.2

Cancel the common factor of $7$ .

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Step 2.1.1.2.1

Move the leading negative in $- \frac{7}{3}$ into the numerator.

$\frac{- 7}{3} (- \frac{y \cdot 3}{7}) = - \frac{7}{3} \cdot 12$

Step 2.1.1.2.2

Move the leading negative in $- \frac{y \cdot 3}{7}$ into the numerator.

$\frac{- 7}{3} \cdot \frac{- y \cdot 3}{7} = - \frac{7}{3} \cdot 12$

Step 2.1.1.2.3

Factor $7$ out of $- 7$ .

$\frac{7 (- 1)}{3} \cdot \frac{- y \cdot 3}{7} = - \frac{7}{3} \cdot 12$

Step 2.1.1.2.4

Cancel the common factor.

$\frac{7 \cdot - 1}{3} \cdot \frac{- y \cdot 3}{7} = - \frac{7}{3} \cdot 12$

Step 2.1.1.2.5

Rewrite the expression.

$\frac{- 1}{3} (- y \cdot 3) = - \frac{7}{3} \cdot 12$

Step 2.1.1.3

Cancel the common factor of $3$ .

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Step 2.1.1.3.1

Factor $3$ out of $- y \cdot 3$ .

$\frac{- 1}{3} (3 \cdot (- y)) = - \frac{7}{3} \cdot 12$

Step 2.1.1.3.2

Cancel the common factor.

$\frac{- 1}{3} (3 \cdot (- y)) = - \frac{7}{3} \cdot 12$

Step 2.1.1.3.3

Rewrite the expression.

$- - y = - \frac{7}{3} \cdot 12$

Step 2.1.1.4

Multiply.

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Step 2.1.1.4.1

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{7}{3} \cdot 12$

Step 2.1.1.4.2

Multiply $y$ by $1$ .

$y = - \frac{7}{3} \cdot 12$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $- \frac{7}{3} \cdot 12$ .

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Step 2.2.1.1

Cancel the common factor of $3$ .

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Step 2.2.1.1.1

Move the leading negative in $- \frac{7}{3}$ into the numerator.

$y = \frac{- 7}{3} \cdot 12$

Step 2.2.1.1.2

Factor $3$ out of $12$ .

$y = \frac{- 7}{3} \cdot (3 (4))$

Step 2.2.1.1.3

Cancel the common factor.

$y = \frac{- 7}{3} \cdot (3 \cdot 4)$

Step 2.2.1.1.4

Rewrite the expression.

$y = - 7 \cdot 4$

Step 2.2.1.2

Multiply $- 7$ by $4$ .

$y = - 28$