# How do you solve abs(v+8)-5=2?

May 23, 2018

See a solution process below:

#### Explanation:

First, add $\textcolor{red}{5}$ to each side of the equation to isolate the absolute value function while keeping the equation balanced:

$\left\mid v + 8 \right\mid - 5 + \textcolor{red}{5} = 2 + \textcolor{red}{5}$

$\left\mid v + 8 \right\mid - 0 = 7$

$\left\mid v + 8 \right\mid = 7$

The absolute value function takes any 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:

$v + 8 = - 7$

$v + 8 - \textcolor{red}{8} = - 7 - \textcolor{red}{8}$

$v + 0 = - 15$

$v = - 15$

• Solution 2:

$v + 8 = 7$

$v + 8 - \textcolor{red}{8} = 7 - \textcolor{red}{8}$

$v + 0 = - 1$

$v = - 1$

The Solution Set Is: $v = \left\{- 15 , - 1\right\}$