How do you solve #abs(5 - x )= - abs(x - 5)#?

1 Answer
KillerBunny
May 12, 2018

#x=5#

Explanation:

Since #5-x = -(x-5)#, you have #|x-5| = |5-x|#. In fact, the absolute value will always consider the positive version of the number. For example, #|-5| = |5| = 5#. or #|-2| = |2| = 2#.

So, in general, #|x|=|-x|# holds.

The equation becomes

#|x-5| = -|x-5#

and thus

#2|x-5|=0 \iff |x-5|#

which ultimately leads to #x-5=0 \implies x=5#

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