How do you solve # 3 | x - 5 | = 12#?

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Answer 1 · 2016-05-13T16:27:23

#x = 1# or #x = 9#

Our strategy will be to isolate the absolute value, and then split the problem into two equations using that for #b>=0#, #|a|=b <=> a=b# or #a=-b#

#3|x-5| = 12#

#=> |x-5| = 12/3 = 4#

#=> x-5 = 4#
or
#x-5 = -4#

#=> x = 4+5 = 9#
or
#x = -4+5 = 1#

Plugging these values in shows them to be correct.

#3|9-5| = 3|4| = 3*4 = 12#
#3|1-5| = 3|-4| = 3*4 = 12#