Question

Solve the following inequality, and express your answer in interval notation.
|2x + 6| + |x + 4| < 17

Answer 1

2x+6< 0
2x < -6
x < -3

x+4 < 0
x < -4

Your challenge is to rewrite your problem without the Absolute Value. With the information just provided (which I am assuming you could do), we have:

For x < -4
-(2x + 6) - (x + 4) < 17

For -4 < x < -3
-(2x + 6) + (x + 4) < 17

For x > -3
(2x + 6) + (x + 4) < 17

Absolute values are just compound equations (inequalities) in disguise, right?