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

May 2, 2018

$- 6 < x < 2$ or $x \in \left(- 6 , 2\right)$

#### Explanation:

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

either $2 x + 4 < 8$

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

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

or $- \left(2 x + 4\right) < 8$

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

or $2 x > - 8 - 4$

or $2 x > - 12$

or $x > - 6$

Hence, $- 6 < x < 2$ or $x \in \left(- 6 , 2\right)$