# How do you solve and write the following in interval notation:  2 ≤ -5x – 13 <7?

Aug 28, 2016

$- 4 < x \le - 3$ and in interval notation it can be written as $\left(- 4 , - 3\right]$

#### Explanation:

Let us divide it in two parts.

1 - $2 \le - 5 x - 13$ or

$5 x \le - 13 - 2$ or

$5 x \le - 15$ or

$x \le - 3$

2 - $- 5 x - 13 < 7$ or

$- 13 - 7 < 5 x$ or

$5 x > - 20$ or

$x > - 4$

Hence solution is $- 4 < x \le - 3$

and in interval notation it can be written as $\left(- 4 , - 3\right]$