Solve for v (|-9+v|)/8=3

$\frac{| - 9 + v |}{8} = 3$

Multiply both sides of the equation by $8$ .

$8 \frac{| - 9 + v |}{8} = 8 \cdot 3$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$8 \frac{| - 9 + v |}{8} = 8 \cdot 3$

Rewrite the expression.

$| - 9 + v | = 8 \cdot 3$

Simplify the right side.

Multiply $8$ by $3$ .

$| - 9 + v | = 24$

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

$- 9 + v = \pm 24$

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.

$- 9 + v = 24$

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

Add $9$ to both sides of the equation.

$v = 24 + 9$

Add $24$ and $9$ .

$v = 33$

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

$- 9 + v = - 24$

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

Add $9$ to both sides of the equation.

$v = - 24 + 9$

Add $- 24$ and $9$ .

$v = - 15$

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

$v = 33, - 15$