# How do you rewrite the inequality abs(x+5)<=9 as a compound inequality?

Jan 2, 2018

$- 14 \le x \le 4$

#### Explanation:

$| x + 5 | \le 9$ so both of the following are true:
If $x + 5$ is positive: $x + 5 \le 9$
If $x + 5$ is negative: $- \left(x + 5\right) \le 9$

Now we solve both inequalities:

$x + 5 \le 9 \setminus \rightarrow x \le 4$

The second inequality is a little more difficult. Remember if you divide by a negative you must change the direction of the inequality:

$- \left(x + 5\right) \le 9$

$x + 5 \ge - 9$

$x \ge - 14$

Now combine the inequalities:

$- 14 \le x \le 4$