# How do you graph and solve |2x + 4|< 8?

Jan 4, 2016

Actually you have to solve two inequalities, depending on $2 x + 4$ being positive or negative.

#### Explanation:

(1)
$2 x + 4 \ge 0 \to x \ge - 2$ the absolute bars do nothing:
$2 x + 4 < 8 \to x < 2$
From these two it follows that $- 2 \le x < 2$

(2)
$2 x + 4 \le 0 \to x \le - 2$ the absolute bars flip the signs
$- 2 x - 4 < 8 \to$ now add $2 x + 4$ on both sides:
$0 < 8 + 2 x + 4 \to$ now subtract $12$:
$- 12 < 2 x \to - 6 < x \to x > - 6$
So $- 6 < x \le - 2$

Adding the two above we get:
$- 6 < x < 2$
graph{|2x+4| [-13.53, 11.78, -2.08, 10.58]}