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

2 Answers
Mar 20, 2016

Answer:

#x=3,-5/3#

Explanation:

Understand that:

enter image source here

#:.# 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#

Mar 20, 2016

Answer:

3 and #-5/3.

Explanation:

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

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

The answer follows..