Solve for v -4/7v=-8 2/3

$- \frac{4}{7} v = - 8 \frac{2}{3}$

Simplify the left side.

Simplify $- \frac{4}{7} v$ .

Combine $v$ and $\frac{4}{7}$ .

$- \frac{v \cdot 4}{7} = - 8 \frac{2}{3}$

Move $4$ to the left of $v$ .

$- \frac{4 v}{7} = - 8 \frac{2}{3}$

Simplify the right side.

Convert $8 \frac{2}{3}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$- \frac{4 v}{7} = - (8 + \frac{2}{3})$

Add $8$ and $\frac{2}{3}$ .

To write $8$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{4 v}{7} = - (8 \cdot \frac{3}{3} + \frac{2}{3})$

Combine $8$ and $\frac{3}{3}$ .

$- \frac{4 v}{7} = - (\frac{8 \cdot 3}{3} + \frac{2}{3})$

Combine the numerators over the common denominator.

$- \frac{4 v}{7} = - \frac{8 \cdot 3 + 2}{3}$

Simplify the numerator.

Multiply $8$ by $3$ .

$- \frac{4 v}{7} = - \frac{24 + 2}{3}$

Add $24$ and $2$ .

$- \frac{4 v}{7} = - \frac{26}{3}$

Multiply both sides of the equation by $- \frac{7}{4}$ .

$- \frac{7}{4} (- \frac{4 v}{7}) = - \frac{7}{4} (- \frac{26}{3})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{7}{4} (- \frac{4 v}{7})$ .

Cancel the common factor of $7$ .

Move the leading negative in $- \frac{7}{4}$ into the numerator.

$\frac{- 7}{4} (- \frac{4 v}{7}) = - \frac{7}{4} (- \frac{26}{3})$

Move the leading negative in $- \frac{4 v}{7}$ into the numerator.

$\frac{- 7}{4} \cdot \frac{- 4 v}{7} = - \frac{7}{4} (- \frac{26}{3})$

Factor $7$ out of $- 7$ .

$\frac{7 (- 1)}{4} \cdot \frac{- 4 v}{7} = - \frac{7}{4} (- \frac{26}{3})$

Cancel the common factor.

$\frac{7 \cdot - 1}{4} \cdot \frac{- 4 v}{7} = - \frac{7}{4} (- \frac{26}{3})$

Rewrite the expression.

$\frac{- 1}{4} (- 4 v) = - \frac{7}{4} (- \frac{26}{3})$

Cancel the common factor of $4$ .

Factor $4$ out of $- 4 v$ .

$\frac{- 1}{4} (4 (- v)) = - \frac{7}{4} (- \frac{26}{3})$

Cancel the common factor.

$\frac{- 1}{4} (4 (- v)) = - \frac{7}{4} (- \frac{26}{3})$

Rewrite the expression.

$- - v = - \frac{7}{4} (- \frac{26}{3})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 v = - \frac{7}{4} (- \frac{26}{3})$

Multiply $v$ by $1$ .

$v = - \frac{7}{4} (- \frac{26}{3})$

Simplify the right side.

Simplify $- \frac{7}{4} (- \frac{26}{3})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{7}{4}$ into the numerator.

$v = \frac{- 7}{4} (- \frac{26}{3})$

Move the leading negative in $- \frac{26}{3}$ into the numerator.

$v = \frac{- 7}{4} \cdot \frac{- 26}{3}$

Factor $2$ out of $4$ .

$v = \frac{- 7}{2 (2)} \cdot \frac{- 26}{3}$

Factor $2$ out of $- 26$ .

$v = \frac{- 7}{2 \cdot 2} \cdot \frac{2 \cdot - 13}{3}$

Cancel the common factor.

$v = \frac{- 7}{2 \cdot 2} \cdot \frac{2 \cdot - 13}{3}$

Rewrite the expression.

$v = \frac{- 7}{2} \cdot \frac{- 13}{3}$

Multiply $\frac{- 7}{2}$ by $\frac{- 13}{3}$ .

$v = \frac{- 7 \cdot - 13}{2 \cdot 3}$

Multiply.

Multiply $- 7$ by $- 13$ .

$v = \frac{91}{2 \cdot 3}$

Multiply $2$ by $3$ .

$v = \frac{91}{6}$

The result can be shown in multiple forms.

Exact Form:

$v = \frac{91}{6}$

Decimal Form:

$v = 15.1\overline{6}$

Mixed Number Form:

$v = 15 \frac{1}{6}$

Solve for v -4/7v=-8 2/3

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