# Question #dd6bd

Sep 18, 2017

$w < - 2 \mathmr{and} w > - 4$

#### Explanation:

$2 | w + 3 | - 1 < 1$
Let start by adding $\textcolor{red}{1}$ to both sides
$2 | w + 3 | - 1 + \textcolor{red}{1} < 1 - \textcolor{red}{1}$
$2 | w + 3 | < 2$
Divide both sides $\textcolor{g r e e n}{2}$
$\frac{2 | w + 3}{\textcolor{g r e e n}{2}} < \frac{2}{\textcolor{g r e e n}{2}}$
$| w + 3 | < 1$
We know $w + 3 < 1 \mathmr{and} w + 3 > - 1$
We have two conditions:
The first one is $w + 3 < 1$
The second one is $w + 3 > - 1$

Let solve the first condition
$w + 3 < 1$
Subtract $\textcolor{p u r p \le}{3}$ from both sides
$w + 3 - \textcolor{p u r p \le}{3} < 1 - \textcolor{p u r p \le}{3}$
$w < - 2$

Let solve the second condition
$w + 3 > - 1$
Subtract $\textcolor{\mathmr{and} a n \ge}{3}$ from both sides
$w + 3 - \textcolor{\mathmr{and} a n \ge}{3} > - 1 - \textcolor{\mathmr{and} a n \ge}{3}$
$w > - 4$

Hence,

$w < - 2 \mathmr{and} w > - 4$