Pre-Algebra Examples

$- \frac{6 v}{7} = - 36$

Step 1

Multiply both sides of the equation by $- \frac{7}{6}$ .

$- \frac{7}{6} (- \frac{6 v}{7}) = - \frac{7}{6} \cdot - 36$

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 $- \frac{7}{6} (- \frac{6 v}{7})$ .

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Step 2.1.1.1

Cancel the common factor of $7$ .

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Step 2.1.1.1.1

Move the leading negative in $- \frac{7}{6}$ into the numerator.

$\frac{- 7}{6} (- \frac{6 v}{7}) = - \frac{7}{6} \cdot - 36$

Step 2.1.1.1.2

Move the leading negative in $- \frac{6 v}{7}$ into the numerator.

$\frac{- 7}{6} \cdot \frac{- 6 v}{7} = - \frac{7}{6} \cdot - 36$

Step 2.1.1.1.3

Factor $7$ out of $- 7$ .

$\frac{7 (- 1)}{6} \cdot \frac{- 6 v}{7} = - \frac{7}{6} \cdot - 36$

Step 2.1.1.1.4

Cancel the common factor.

$\frac{7 \cdot - 1}{6} \cdot \frac{- 6 v}{7} = - \frac{7}{6} \cdot - 36$

Step 2.1.1.1.5

Rewrite the expression.

$\frac{- 1}{6} (- 6 v) = - \frac{7}{6} \cdot - 36$

Step 2.1.1.2

Cancel the common factor of $6$ .

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Step 2.1.1.2.1

Factor $6$ out of $- 6 v$ .

$\frac{- 1}{6} (6 (- v)) = - \frac{7}{6} \cdot - 36$

Step 2.1.1.2.2

Cancel the common factor.

$\frac{- 1}{6} (6 (- v)) = - \frac{7}{6} \cdot - 36$

Step 2.1.1.2.3

Rewrite the expression.

$- - v = - \frac{7}{6} \cdot - 36$

Step 2.1.1.3

Multiply.

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Step 2.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 v = - \frac{7}{6} \cdot - 36$

Step 2.1.1.3.2

Multiply $v$ by $1$ .

$v = - \frac{7}{6} \cdot - 36$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $- \frac{7}{6} \cdot - 36$ .

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Step 2.2.1.1

Cancel the common factor of $6$ .

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Step 2.2.1.1.1

Move the leading negative in $- \frac{7}{6}$ into the numerator.

$v = \frac{- 7}{6} \cdot - 36$

Step 2.2.1.1.2

Factor $6$ out of $- 36$ .

$v = \frac{- 7}{6} \cdot (6 (- 6))$

Step 2.2.1.1.3

Cancel the common factor.

$v = \frac{- 7}{6} \cdot (6 \cdot - 6)$

Step 2.2.1.1.4

Rewrite the expression.

$v = - 7 \cdot - 6$

Step 2.2.1.2

Multiply $- 7$ by $- 6$ .

$v = 42$