Solve the Absolute Value Inequality for v -10|v+2|=-70

$- 10 | v + 2 | = - 70$

Divide each term in $- 10 | v + 2 | = - 70$ by $- 10$ and simplify.

Divide each term in $- 10 | v + 2 | = - 70$ by $- 10$ .

$\frac{- 10 | v + 2 |}{- 10} = \frac{- 70}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 | v + 2 |}{- 10} = \frac{- 70}{- 10}$

Divide $| v + 2 |$ by $1$ .

$| v + 2 | = \frac{- 70}{- 10}$

Simplify the right side.

Divide $- 70$ by $- 10$ .

$| v + 2 | = 7$

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$v + 2 = \pm 7$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$v + 2 = 7$

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

Subtract $2$ from both sides of the equation.

$v = 7 - 2$

Subtract $2$ from $7$ .

$v = 5$

Next, use the negative value of the $\pm$ to find the second solution.

$v + 2 = - 7$

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

Subtract $2$ from both sides of the equation.

$v = - 7 - 2$

Subtract $2$ from $- 7$ .

$v = - 9$

The complete solution is the result of both the positive and negative portions of the solution.

$v = 5, - 9$