How do you solve # |4x-2|=6#?

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Answer 1 · 2016-04-09T22:20:28

#x=-1,2#

The procedure is to separate the equation in two branches:

#1) if 4x-2>0:#

#|4x-2|=6 and 4x-2>0#

#4x-2=6 and 4x>2#

#4x=6+2 and x>2/4#

#x=8/4 and x>2/4#

#x=2 and x>1/2#

#x=2#

#2) if 4x-2<0:#

#|4x-2|=6 and 4x-2<0#

#-4x+2=6 and 4x<2#

#-4x=6-2 and x<2/4#

#x=-4/4 and x<2/4#

#x=-1 and x<1/2#

#x=-1#