How do you solve #3abs(w/2+5)< 18#?

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Answer 1 · 2015-04-22T18:45:47

#3abs(w/2+5) < 18#
could be written
#abs(w/2+5)<6#

Two cases need to be considered

Case 1:
#(w/2+5)<0#
#rarr w<-10#

#abs(w/2+5) < 6#
becomes
#-w/2-5<6#

#-w/2 <11#

#w > -22#

Case 1 gives us
#w<-10# and #w > -22#
#w epsilon (-22,-10)#

Case 2:
#(w/2+5)>=0#
#rarr w >= -10#

#abs(w/2+5) < 6#
becomes
#w/2+5<6#

#w/2<1#
#w<2#

Case 2 gives us
#w>=-10# and #w<2#
#w epsilon [-10,+2)#

Union of the two cases:
#w epsilon (-22,-10)uuw epsilon [-10,+2) #
gives a final solution

#w epsilon (-22,+2)#