How do you find the solution set for the equation |x-6|=7?

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Answer 1 · 2016-10-19T07:15:03

#x in {-1, 13}#

Note that we define the absolute value function as

#|a| = {(a if a>= 0), (-a if a < 0):}#

so we consider two cases:

Case 1) #x-6 >= 0#

#=> |x-6| = x-6#

#=> x-6 = 7#

#=> x-6 + 6 = 7+6#

#=> x = 13#

Case 2) #x-6 < 0#

#=> |x-6| = -(x-6)#

#=> -(x-6) = 7#

#=> -x+6 = 7#

#=> -x+6-6 = 7-6#

#=> -x = 1#

#=> x = -1#

As these cases account for all possibilities, we have found all possible solutions.

#x in {-1, 13}#