How do you solve #52= 7| x - 2| - 4#?

1 Answer
smendyka
Nov 27, 2016

#x = 10# and #x = -6#

Explanation:

First, add #4# to each side of the equation and then divide each side of the equation by #7# to keep the equation balanced and to isolate the absolute value term:

#52 + 4 = 7abs(x - 2) - 4 + 4#

#56 = 7abs(x - 2)#

#56/7 = (7abs(x - 2))/7#

#abs(x - 2) = 8#

Now we must solve #x - 2# for #8# and #-8# because the absolute value function will turn the result positive:

#x - 2 = 8#

#x - 2 + 2 = 8 + 2#

#x = 10#

and

#x - 2 = -8#

#x - 2 + 2 = -8 + 2#

#x = -6#

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