How do you solve #abs(3x+2)=14#?

1 Answer
Jul 16, 2015

Answer:

#color(red)(x = 4)# and # color(red)(x = -16/3)#.

Explanation:

We need to write two different equations without the absolute value symbols and solve for #x#.

These equations would be

(1): #(3x+2) = 14#
(2): #-(3x+2) = 14#

Solve Equation 1:

#3x+2 = 14#

Subtract #2# from each side.

#3x = 12#

Divide each side by #3#.

#x = 4#

Solve Equation 2.

#−(3x+2) = 14#

Remove parentheses.

#−3x−2= 14#

Add #2# to each side.

#-3x = 16#

Divide each side by #-3#.

#x = -16/3#

The solutions are #x = 4# and #x = -16/3#.

Check:

If #x = 4#,

#|3x+2|=14#
#|3×4 +2|= 14#
#|12 + 2| = 14#
#|14| =14#
#14=14#

If #x= -16/3#,

#|3x+2|=14#
#|3×(-16/3) + 2| = 14#
#|-16 + 2| = 14#
#|-14| = 14#
#14 = 14#