How do you solve and write the following in interval notation: abs(2x+9) ≤ 3?

Feb 22, 2017

The solution is $x \in \left[- 6 , - \frac{9}{2}\right] \cup \left[- \frac{9}{2} , - 3\right]$

Explanation:

There are 2 solutions to this equation

$2 x + 9 \le 3$ and $- 2 x - 9 \le 3$

$2 x \le - 6$ and $2 x \ge - 12$

$x \le - 3$ and $x \ge - 6$

We need to solve

$2 x + 9 = 0$

$x = - \frac{9}{2}$

Therefore, the solutions are

$x \in \left[- 6 , - \frac{9}{2}\right] \cup \left[- \frac{9}{2} , - 3\right]$