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

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Answer 1 · 2015-08-27T23:39:56

#x<16#
#x> -20#

#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#