How do you graph and solve #|1/2x-45|>80#?

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Answer 1 · 2018-05-21T06:25:42

The solution is #x in (-oo,-70) uu(250,+oo)#

This is an inequality with absolute values

#|1/2x-45|>80#

The solutions are

#{(1/2x-45>80),(-1/2x+45>80):}#

#<=>#, #{(1/2x>80+45),(1/2x<45-80):}#

#<=>#, #{(1/2x>125),(1/2x<-35):}#

#<=>#, #{(x>250),(x<-70):}#

The solution is #x in (-oo,-70) uu(250,+oo)#

The graph is as follows

graph{|1/2x-45|-80 [-133, 348, -106.4, 134.2]}