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

1 Answer
sente
Apr 28, 2016

#x=-1/2#

Explanation:

#|x+3| = |x-2|#

#=> x+3 = |x-2|#
or
#-(x+3) = |x-2|#

#=> x+3 = x-2#
or
#x+3 = -(x-2)#
or
#-(x+3)=x-2#
or
#-(x+3)=-(x-2)#

The first and fourth equations have no solution as you can cancel #x# (or #-x#) from both sides to obtain #2=-3#, which is a contradiction.

The second and third equations have the same solution, as one can be obtained from the other by multiplying both sides by #-1#. Then, we may simply solve

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

#=> x+3 = -x+2#

#=>2x=-1#

#:.x = -1/2#

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