# How do you solve and write the following in interval notation: | x | – 2 <7?

Jun 25, 2016

First of all we write

$| x | - 2 < 7$

$| x | < 9$

then we remove the absolute value remembering that we have to use both signs $\setminus \pm$ and when we use the $-$ sign we have to invert the inequality.

$| x | < 9$

$x < 9$ and $x > - 9$

This tell us that $x$ can assume any value between $- 9$ and $9$ that can be written as

$- 9 < x < 9$
or
$x \setminus \in \left(- 9 , 9\right)$.