# How do you solve |x+2|=5?

Mar 20, 2016

There are usually two answers, depending on the function inside the absolute brackets being positive or negative.

#### Explanation:

(1) $x \ge - 2 \to x + 2 \ge 0$ the equation is unchanged

$\to x + 2 = 5 \to x = 3$

(2) $x < - 2 \to x + 2 < 0$ then the signs are 'flipped' to make the function as a whole positive:

$\to - \left(x + 2\right) = - x - 2 = 5 \to - x = 7 \to x = - 7$
graph{|x+2| [-8.17, 11.83, -2.16, 7.84]}