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.

$x in {-1, 13}$