How do you solve #2abs(3x - 4) + 8=6#?

Question

1982 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-26T15:52:23

Solve as you would any equation, then make #|3x-4|# positive, #3x-4=-1#, and negative, #-(3x-4)=-1#. Solve for #x#.

#2|3x-4|+8=6#

Subtract #8# from both sides.

#2|3x-4|=-2#

Divide both sides by #2#.

#|3x-4|=-1#

The quantity inside the absolute value symbols can be positive or negative: #3x-4=-1# and #-(3x-4)=-1#

When #|3x-4|# is positive:

#3x-4=-1#

Add #4# to both sides of the equation.

#3x=3#

Divide both sides by #3#.

#x=1#

When #|3x-4|# is negative:

#-(3x-4)=-1#

#-3x+4=-1#

Subtract #4# from both sides.

#-3x=-5#

Divide both sides by #-3#.

#x=5/3#

Answer: #x=1,5/3#