Solve for v 5/6v+7=-3

$\frac{5}{6} v + 7 = - 3$

Step 1

Combine $\frac{5}{6}$ and $v$ .

$\frac{5 v}{6} + 7 = - 3$

Step 2

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

Subtract $7$ from both sides of the equation.

$\frac{5 v}{6} = - 3 - 7$

Subtract $7$ from $- 3$ .

$\frac{5 v}{6} = - 10$

Step 3

Multiply both sides of the equation by $\frac{6}{5}$ .

$\frac{6}{5} \cdot \frac{5 v}{6} = \frac{6}{5} \cdot - 10$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{6}{5} \cdot \frac{5 v}{6}$ .

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6}{5} \cdot \frac{5 v}{6} = \frac{6}{5} \cdot - 10$

Rewrite the expression.

$\frac{1}{5} (5 v) = \frac{6}{5} \cdot - 10$

Cancel the common factor of $5$ .

Factor $5$ out of $5 v$ .

$\frac{1}{5} (5 (v)) = \frac{6}{5} \cdot - 10$

Cancel the common factor.

$\frac{1}{5} (5 v) = \frac{6}{5} \cdot - 10$

Rewrite the expression.

$v = \frac{6}{5} \cdot - 10$

Simplify the right side.

Simplify $\frac{6}{5} \cdot - 10$ .

Cancel the common factor of $5$ .

Factor $5$ out of $- 10$ .

$v = \frac{6}{5} \cdot (5 (- 2))$

Cancel the common factor.

$v = \frac{6}{5} \cdot (5 \cdot - 2)$

Rewrite the expression.

$v = 6 \cdot - 2$

Multiply $6$ by $- 2$ .

$v = - 12$