# How do you graph and solve |1/2x-45|>80?

May 21, 2018

The solution is $x \in \left(- \infty , - 70\right) \cup \left(250 , + \infty\right)$

#### Explanation:

This is an inequality with absolute values

$| \frac{1}{2} x - 45 | > 80$

The solutions are

$\left\{\begin{matrix}\frac{1}{2} x - 45 > 80 \\ - \frac{1}{2} x + 45 > 80\end{matrix}\right.$

$\iff$, $\left\{\begin{matrix}\frac{1}{2} x > 80 + 45 \\ \frac{1}{2} x < 45 - 80\end{matrix}\right.$

$\iff$, $\left\{\begin{matrix}\frac{1}{2} x > 125 \\ \frac{1}{2} x < - 35\end{matrix}\right.$

$\iff$, $\left\{\begin{matrix}x > 250 \\ x < - 70\end{matrix}\right.$

The solution is $x \in \left(- \infty , - 70\right) \cup \left(250 , + \infty\right)$

The graph is as follows

graph{|1/2x-45|-80 [-133, 348, -106.4, 134.2]}