# How do you solve and graph abs(5-2x)=13?

May 26, 2018

The solutions are $S = \left\{- 4 , 9\right\}$

#### Explanation:

The equation is

$| 5 - 2 x | = 13$

The solutions are

$\left\{\begin{matrix}5 - 2 x = 13 \\ - 5 + 2 x = 13\end{matrix}\right.$

$\iff$, $\left\{\begin{matrix}2 x = 5 - 13 = - 8 \\ 2 x = 13 + 5 = 18\end{matrix}\right.$

$\iff$, $\left\{\begin{matrix}x = - 4 \\ x = 9\end{matrix}\right.$

The solutions are $S = \left\{- 4 , 9\right\}$

The graph is as follows

graph{|5-2x|-13 [-28.65, 29.1, -15, 13.87]}