Pre-Algebra Examples

$- \frac{3}{2} v = - 15$

Step 1

Multiply both sides of the equation by $- \frac{2}{3}$ .

$- \frac{2}{3} (- \frac{3}{2} v) = - \frac{2}{3} \cdot - 15$

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 $- \frac{2}{3} (- \frac{3}{2} v)$ .

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Step 2.1.1.1

Combine $v$ and $\frac{3}{2}$ .

$- \frac{2}{3} (- \frac{v \cdot 3}{2}) = - \frac{2}{3} \cdot - 15$

Step 2.1.1.2

Cancel the common factor of $2$ .

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Step 2.1.1.2.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{- 2}{3} (- \frac{v \cdot 3}{2}) = - \frac{2}{3} \cdot - 15$

Step 2.1.1.2.2

Move the leading negative in $- \frac{v \cdot 3}{2}$ into the numerator.

$\frac{- 2}{3} \cdot \frac{- v \cdot 3}{2} = - \frac{2}{3} \cdot - 15$

Step 2.1.1.2.3

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{3} \cdot \frac{- v \cdot 3}{2} = - \frac{2}{3} \cdot - 15$

Step 2.1.1.2.4

Cancel the common factor.

$\frac{2 \cdot - 1}{3} \cdot \frac{- v \cdot 3}{2} = - \frac{2}{3} \cdot - 15$

Step 2.1.1.2.5

Rewrite the expression.

$\frac{- 1}{3} (- v \cdot 3) = - \frac{2}{3} \cdot - 15$

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 $- v \cdot 3$ .

$\frac{- 1}{3} (3 \cdot (- v)) = - \frac{2}{3} \cdot - 15$

Step 2.1.1.3.2

Cancel the common factor.

$\frac{- 1}{3} (3 \cdot (- v)) = - \frac{2}{3} \cdot - 15$

Step 2.1.1.3.3

Rewrite the expression.

$- - v = - \frac{2}{3} \cdot - 15$

Step 2.1.1.4

Multiply.

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Step 2.1.1.4.1

Multiply $- 1$ by $- 1$ .

$1 v = - \frac{2}{3} \cdot - 15$

Step 2.1.1.4.2

Multiply $v$ by $1$ .

$v = - \frac{2}{3} \cdot - 15$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $- \frac{2}{3} \cdot - 15$ .

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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 $- \frac{2}{3}$ into the numerator.

$v = \frac{- 2}{3} \cdot - 15$

Step 2.2.1.1.2

Factor $3$ out of $- 15$ .

$v = \frac{- 2}{3} \cdot (3 (- 5))$

Step 2.2.1.1.3

Cancel the common factor.

$v = \frac{- 2}{3} \cdot (3 \cdot - 5)$

Step 2.2.1.1.4

Rewrite the expression.

$v = - 2 \cdot - 5$

Step 2.2.1.2

Multiply $- 2$ by $- 5$ .

$v = 10$