# How do you solve this absolute-value inequality 6abs(2x + 5 )> 66?

Apr 3, 2015

Answer: $x < - 8 \cup x > 3$

Solution:
$6 | 2 x + 5 | > 66$

$\implies | 2 x + 5 | > 11$

By definition, $| x | > k$ where $k$ is a constant, means:
$x < - k \cup x > k$
This implies,

$2 x + 5 < - 11 \cup 2 x + 5 > 11$

Case1: 2x + 5 < -11

$\implies 2 x < - 16 \implies x < - 8$

Case2: 2x + 5 > 11

$\implies 2 x > 6 \implies x > 3$