How do you solve # 2abs(x -5) > 32 #?

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Answer 1 · 2015-04-29T19:00:54

We can divide both sides by 2 to get

#abs(x-5) > 32/2#

#->abs(x-5) > 16#

This tells us two things:
Either #x - 5 > 16# or #x-5<-16#

# x > 16 +5# or #x < -16+5#

#color(green)(x>21# or #color(green)(x<-11#

To verify your answer , choose appropriate values of #x# and see if the inequality is satisfied

Say #x = 25#

Left hand side = #2*abs(25-5) = 2*20 = 40# (#>32#)

Say #x = -12#

Left hand side = #2*abs(-12-5) = 2*abs(-17) = 2*17 = 34# (#>32#)