How do you solve #-2< absx<4#?

1 Answer
MeneerNask
Apr 6, 2015

The inequality is partly senseless since #|x|# can never be below #0#

So we are left with #0<=|x|<4#, which can mean two things:

(1) For positive #x#'s the absolute has no effect:
#x>=0 -> x<4-> 0<=x<4#

(2) For negative #x#'s the sign changes:
#x<0->-x<4->-4<x<=0#

graph{|x| [-12.34, 16.13, -2.05, 12.19]}

So the total solution space is: #-4<x<+4# (see graph)

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