# How do you solve -2<x+2<5?

##### 2 Answers
Apr 20, 2018

See a solution process below

#### Explanation:

$- 2 < x + 2 < 5$

Cross $2$ to the right hand side..

$- 2 < x < 5 - 2$

$- 2 < x < 3$

Hence;

$x < 3$

The statement above indicates that $x$ is less than $3$

$- 2 < x \mathmr{and} x > - 2$

The statement above means that $- 2$ is less than $x \mathmr{and} x$ is greater than $- 2$

Apr 20, 2018

$x \in \left(- 4 , 3\right)$

#### Explanation:

$\text{subtract 2 from each interval}$

$- 2 \textcolor{red}{- 2} < x \cancel{+ 2} \cancel{\textcolor{red}{- 2}} < 5 \textcolor{red}{- 2}$

$\Rightarrow - 4 < x < 3$

$\Rightarrow x \in \left(- 4 , 3\right) \leftarrow \textcolor{b l u e}{\text{in interval notation}}$