Question

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

Answer 1

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

Explanation:

(1)
`2x+4>=0->x>=-2` the absolute bars do nothing:
`2x+4<8->x<2`
From these two it follows that `-2<=x<2`

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

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