How do you solve the absolute value inequality #abs(x+8)+4>0#?

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Answer 1 · 2018-07-27T09:51:39

#x\in \mathbb R#

Given inequality:

#|x+8|+4>0#

Case 1: When #x\le -8# then #|x+8|=-(x+8)#

#\therefore -(x+8)+4>0#

#-x-4>0#

#x<-4#

The solution is #x\le -8#

Case 2: When #x> -8# then #|x+8|=x+8#

#\therefore x+8+4>0#

#x+12>0#

#x > -12#

The solution is #x > -8#

Hence the total solution is

#x\le -8 \ \ \or \ \ x> -8#

#x in (-\infty, -8]\cup(-8, \infty)#

#x\in (-\infty, \infty)#

#x\in \mathbb R#