Question

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

Answer 1

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

So we are left with `0<=|x|<4`, which can mean two things:

(1) For positive `x`'s the absolute has no effect:
`x>=0 -> x<4-> 0<=x<4`

(2) For negative `x`'s the sign changes:
`x<0->-x<4->-4<x<=0`

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

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