How do you solve and graph #4<y+2<-3(y-2)+24#?

1 Answer
Alan P.
Jul 24, 2015

#2 < y < 7#
#color(white)("XXXX")#(see below for number line graph)

Explanation:

Treat the two inequalities separately then recombine.

Inequality 1: #color(white)("XXXX")##4 < y + 2#
Subtracting #2# from both sides gives:
#color(white)("XXXX")##2 < y#

Inequality 2: #color(white)("XXXX")##y + 2 < -3(y - 2) +24#
Simplifying the #-3(y-2)# term:
#color(white)("XXXX")##y + 2 < -3y +6 + 24#
Basic arithmetic
#color(white)("XXXX")##y + 2 < -3y +30#
Add #(3y-2)# to both sides
#color(white)("XXXX")##4y < 28#
Divide both sides by #4#
#color(white)("XXXX")##y < 7#

Recombining
#color(white)("XXXX")##2 < y < 7#

enter image source here

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