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

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 $b \ge 0$, $| a | = b \iff a = b$ or $a = - b$

$3 | x - 5 | = 12$

$\implies | x - 5 | = \frac{12}{3} = 4$

$\implies x - 5 = 4$
or
$x - 5 = - 4$

$\implies x = 4 + 5 = 9$
or
$x = - 4 + 5 = 1$

Plugging these values in shows them to be correct.

$3 | 9 - 5 | = 3 | 4 | = 3 \cdot 4 = 12$
$3 | 1 - 5 | = 3 | - 4 | = 3 \cdot 4 = 12$