# How do you solve and write the following in interval notation: -2|3x+5|+7>=-13?

May 28, 2016

$x \in \left[- 5 , \frac{5}{3}\right]$

#### Explanation:

$- 2 | 3 x + 5 | \ge -$. Division by $- 2$ would reverse the inequality sign.

So, $| 3 x + 5 | \le 10$

This is the combined inequality for the pair

$3 x + 5 \le 10 \mathmr{and} - \left(3 x + 5\right) \le 10$

Accordingly, $3 x \le 5 \mathmr{and} 3 x \ge - 15$.

Thus, $x \le \frac{5}{3} \mathmr{and} x \ge - 5$..