# What is the solution set for abs(2x – 4) = 10?

Aug 29, 2015

$x = - 3$ or $x = 7$

#### Explanation:

Case 1: $2 x - 4 \ge 0$
$\left\mid 2 x - 4 \right\mid = 10$
$\rightarrow \textcolor{w h i t e}{\text{XXX}} 2 x - 4 = 10$
$\rightarrow \textcolor{w h i t e}{\text{XXX}} 2 x = 14$
$\rightarrow \textcolor{w h i t e}{\text{XXX}} x = 7$

Case 2: $2 x - 4 < 0$
$\left\mid 2 x - 4 \right\mid = 10$
$\rightarrow \textcolor{w h i t e}{\text{XXX}} 4 - 2 x = 10$
$\rightarrow \textcolor{w h i t e}{\text{XXX}} - 2 x = 6$
$\rightarrow \textcolor{w h i t e}{\text{XXX}} x = - 3$