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

1 Answer
May 21, 2018

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

Explanation:

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]}