How do you solve #-abs(5/3y+4)>2/5#?

1 Answer
Daniel L.
Apr 22, 2015

The answer is #x in (-oo;-2 16/25) uu (-2 4/25;+oo)#

First you have to simplify the absolute value. To do this you use the identity

#|x|>a iff (x<-a vv x>a )#
So you get a set of linear inequalities

#5/3 y +4 > 2/5 vv 5/3 y +4 < - 2/5#

To simplify the inequalities you can multiply both sides by 15 to get rid of the fractions.

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