# How do you solve abs(-9+v)/8=3?

##### 1 Answer
Aug 17, 2017

See a solution process below:

#### Explanation:

First, multiply each side of the equation by $\textcolor{red}{8}$ to isolate the absolute value function while keeping the equation balanced:

$\textcolor{red}{8} \times \frac{\left\mid - 9 + v \right\mid}{8} = \textcolor{red}{8} \times 3$

$\cancel{\textcolor{red}{8}} \times \frac{\left\mid - 9 + v \right\mid}{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}}} = 24$

$\left\mid - 9 + v \right\mid = 24$

The absolute value function takes any negative or positive term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

Solution 1:

$- 9 + v = - 24$

$\textcolor{red}{9} - 9 + v = \textcolor{red}{9} - 24$

$0 + v = - 15$

$v = - 15$

Solution 2:

$- 9 + v = 24$

$\textcolor{red}{9} - 9 + v = \textcolor{red}{9} + 24$

$0 + v = 33$

$v = 33$

The Solutions Are: $v = - 15$ and $v = 33$