Solve the Absolute Value Inequality for v |v+8|-5=2

$| v + 8 | - 5 = 2$

Move all terms not containing $| v + 8 |$ to the right side of the equation.

Add $5$ to both sides of the equation.

$| v + 8 | = 2 + 5$

Add $2$ and $5$ .

$| v + 8 | = 7$

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

$v + 8 = \pm 7$

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.

$v + 8 = 7$

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

Subtract $8$ from both sides of the equation.

$v = 7 - 8$

Subtract $8$ from $7$ .

$v = - 1$

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

$v + 8 = - 7$

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

Subtract $8$ from both sides of the equation.

$v = - 7 - 8$

Subtract $8$ from $- 7$ .

$v = - 15$

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

$v = - 1, - 15$