# How do you solve -2< absx<4?

Apr 6, 2015

The inequality is partly senseless since $| x |$ can never be below $0$

So we are left with $0 \le | x | < 4$, which can mean two things:

(1) For positive $x$'s the absolute has no effect:
$x \ge 0 \to x < 4 \to 0 \le x < 4$

(2) For negative $x$'s the sign changes:
$x < 0 \to - x < 4 \to - 4 < x \le 0$

graph{|x| [-12.34, 16.13, -2.05, 12.19]}

So the total solution space is: $- 4 < x < + 4$ (see graph)