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.

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

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