# How do you solve and write the following in interval notation: |x + 5| <18?

Sep 19, 2016

$\left(- 23 , 13\right)$

#### Explanation:

$\left\mid x + 5 \right\mid < 18$

Write as two inequalities:

$x + 5 < 18$ and $\textcolor{w h i t e}{a a a} x + 5 > - 18$

$\textcolor{w h i t e}{a} - 5 \textcolor{w h i t e}{a} - 5 \textcolor{w h i t e}{a a a a a a a a} - 5 \textcolor{w h i t e}{a a a a} - 5$

$x < 13 \textcolor{w h i t e}{a a a a}$and$\textcolor{w h i t e}{a a a a a a} x > - 23$

In interval notation: $\left(- 23 , 13\right)$

Another way to look at it:

Write as one inequality:

$- 18 < x + 5 < 18$
$- 5 \textcolor{w h i t e}{a a a a a} - 5 \textcolor{w h i t e}{a} - 5$

$- 23 < \textcolor{w h i t e}{a a} x \textcolor{w h i t e}{a a} < 13$

Interval notation is easier to write when the problem is solved this way because the $x$ is "between" the numbers in the interval.
$\left(- 23 , 13\right)$