How do you solve 3|x−5|=12?

1 Answer
sente
May 13, 2016

x=1 or x=9

Explanation:

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|=123=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

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