# How do you solve and graph abs(x-4)<9?

Mar 18, 2018

The solution is $x \in \left(5 , 13\right)$

#### Explanation:

There are $2$ solutions for Inequalities with absolute values

$| x - 4 | < 9$

$x - 4 < 9$ and $- x + 4 < 9$

Therefore,

$x < 13$ and $x > 5$

The solutions are

${S}_{1} = x \in \left(- \infty , 13\right)$

and ${S}_{2} = x \in \left(5 , + \infty\right)$

The solution

$S = {S}_{1} \cap {S}_{2}$

$S = x \in \left(5 , 13\right)$

See the graph below

graph{|x-4|-9 [-18.02, 18.03, -9.01, 9.01]}