# How do you solve and write the following in interval notation: 4 ≤ 3 − x <8?

Aug 7, 2017

$\left(- 5 , - 1\right]$

#### Explanation:

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

$4 - 3 \le 3 - 3 - x < 8 - 3$

$\Rightarrow 1 \le - x < 5$

$\text{multiply all 3 intervals by - 1 remembering to reverse the}$
$\text{inequality signs}$

$\Rightarrow - 1 \ge x > - 5 \leftarrow \textcolor{red}{\text{ reverse signs}}$

$\text{in interval notation as } \left(- 5 , - 1\right]$