# How do you solve the inequality abs(x + 2) <=11?

##### 1 Answer
Mar 27, 2018

Determine your boundary conditions to solve for the minimum and maximum values of x, then write out the final inequality $- 13 \le x \le 9$

#### Explanation:

We need to determine the boundaries where this inequality is true. Because we're dealing with an absolute value, the two scenarios look like this:

$x + 2 \le 11$

$x + 2 \ge - 11$

Notice I flipped the sign for the opposite boundary. This is because we're dealing with the negative solution, and when you flip a sign on an inequality, the direction of the comparator flips as well.

Now, let's solve for x in both expressions:

$x + 2 \le 11$

$x \cancel{+ 2 - 2} \le 11 - 2$

$\textcolor{red}{x \le 9}$

$x + 2 \ge - 11$

$x \cancel{+ 2 - 2} \ge - 11 - 2$

$\textcolor{b l u e}{x \ge - 13}$

Now that we know our bounds, we can write it as a single inequality:

$\textcolor{g r e e n}{- 13 \le x \le 9}$