Question

What is the solution set for `abs(2x + 4)< 8`?

Answer 1

`-6 < x < 2` or `x in (-6,2)`

Explanation:

As `|2x+4|<8`, then

either `2x+4<8`

i.e. `2x<8-4`

or `2x<4` i.e, `x<2`

or `-(2x+4)<8`

i.e. `2x+4> -8`

or `2x> -8-4`

or `2x> -12`

or `x> -6`

Hence, `-6 < x < 2` or `x in (-6,2)`