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

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Answer 1 · 2015-07-16T23:58:28

#color(red)(x = 0)# and # color(red)(x = -4/3)#.

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

These equations would be

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

Solve Equation 1:

#3x+2 = 2#

Subtract #2# from each side.

#3x = 0#

Divide each side by #3#.

#x = 0#

Solve Equation 2.

#−(3x+2) = 2#

Remove parentheses.

#−3x−2= 2#

Add #2# to each side.

#-3x = 4#

Divide each side by #-3#.

#x = -4/3#

The solutions are #x = 0# and #x = -4/3#.

Check:

If #x = 0#,

#|3x+2|=2#
#|3×0 +2|= 2#
#|0 + 2| = 2#
#|2| =2#
#2=2#

If #x= -4/3#,

#|3x+2|=2#
#|3×(-4/3) + 2| = 2#
#|-4 + 2| = 2#
#|-2| = 2#
#2 = 2#