How do you solve the inequality: abs(x + 2) < 18?

1 Answer
Aug 27, 2015

x<16
x> -20

Explanation:

abs(x+2)<18

Separate the inequality into two inequalities, one positive and one negative.

x+2<18 and -(x+2)<18

Positive Inequality

x+2<18

Subtract 2 from both sides.

x<18-2=

x<16

Negative Inequality

-(x+2)<18

-x-2<18

Add 2 to both sides.

-x<18+2=

-x<20

Multiply both sides times -1.

x> -20

Solutions for x.

x<16
x> -20