# How do you solve the inequality -4 < 2 + x <1?

Mar 21, 2018

$x \in \left(- 6 , - 1\right)$

#### Explanation:

Add $- 2$ to each term

$- 4 - 2 < 2 - 2 + x < 1 - 2$ or

$- 6 < x < - 1$ so

$x \in \left(- 6 , - 1\right)$

Mar 21, 2018

$- 6 < x < - 1$

#### Explanation:

$\text{Isolate x in the middle interval by subtracting 2 from all 3}$
$\text{intervals}$

$- 4 \textcolor{red}{- 2} < \cancel{2} \cancel{\textcolor{red}{- 2}} + x < 1 \textcolor{red}{- 2}$

$\Rightarrow - 6 < x < - 1$