# How do you solve 2|x + 4| = 8?

Aug 3, 2017

See a solution process below:

#### Explanation:

First, divide each side of the equation by $\textcolor{red}{2}$ to isolate the absolute value function while keeping the equation balanced:

$\frac{2 \left\mid x + 4 \right\mid}{\textcolor{red}{2}} = \frac{8}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \left\mid x + 4 \right\mid}{\cancel{\textcolor{red}{2}}} = 4$

$\left\mid x + 4 \right\mid = 4$

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

$x + 4 = - 4$

$x + 4 - \textcolor{red}{4} = - 4 - \textcolor{red}{4}$

$x + 0 = - 8$

$x = - 8$

Solution 2

$x + 4 = 4$

$x + 4 - \textcolor{red}{4} = 4 - \textcolor{red}{4}$

$x + 0 = 0$

$x = 0$

The solutions are: $x = - 8$ and $x = 0$