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

1 Answer
Apr 3, 2015

Answer: x < -8 uu x > 3

Solution:
6|2x + 5|> 66

=> |2x + 5|> 11

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

2x + 5 < -11 uu 2x + 5 > 11

Case1: 2x + 5 < -11

=> 2x < -16 => x< -8

Case2: 2x + 5 > 11

=> 2x > 6 => x > 3