How do you solve #abs(x+3)=3x+1#?

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Answer 1 · 2016-09-06T19:45:25

The solution set is #{ 1}#.

Case 1: The absolute value is positive

#x + 3 = 3x + 1#

#-2x = -2#

#x = 1#

Case 2: The absolute value is negative

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

#-x - 3 = 3x + 1#

#-3 - 1 = 4x#

#-4 = 4x#

#x =-1#

However, checking, you will find #x = -1# is extraneous.

Hence, the solution set is #{1}#.

Hopefully this helps!