What is the solution set of the equation #|3-2x| = 5#?

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Answer 1 · 2018-07-27T14:03:26

#x \ in{-1, 4}#

Given equation:

#|3-2x|=5#

#3-2x=\pm5#

#2x=3\pm5#

#x=\frac{3\pm5}{2}#

#x=4, -1#

#x\in {-1, 4}#

Answer 2 · 2018-07-27T14:09:21

The solutions are #S={-1,4}#

#3-2x=0#

#=>#, #x=3/2#

There are #2# possibilities to consider

Firstly

#-3+2x=5#

#=>#, #2x=8#

#x=4#

And Secondly

#3-2x=5#

#=>#, #2x=3-5#

#x=-1#

The solutions are #S={-1,4}#

graph{|3-2x|-5 [-10, 10, -5, 5]}