How do you solve # 2| 3x - 2 | = 14#?

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Answer 1 · 2016-03-20T05:37:22

#x=3,-5/3#

Understand that:

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#:.# Absolute values are always mean the distance from #0#

eg,#|-7|=7,|4|=4#

#color(blue)(2|3x-2|=14#

Divide both sides by #2#

#rarr(cancel2|3x-2|)/cancel2=14/2#

#rarr|3x-2|=7#

Now we can write that

#color(brown)(3x-2=7,3x-2=-7#

Solve for both the equations

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~#

#color(orange)(3x-2=7#

#rarr3x=7+2#

#rarr3x=9#

#color(green)(rArrx=9/3=3#

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~#

#color(indigo)(3x-2=-7#

#rarr3x=-7+2#

#rarr3x=-5#

#color(green)(rArrx=-5/3#

Answer 2 · 2016-03-20T05:44:57

3 and #-5/3.

#|3x-2|=7# is the combined equation for the couple

#3x-2 = 7 and 2-3x=7#

The answer follows..