# How do you solve  |x - 2| + 10 = 12?

Jun 30, 2016

The Solns. are $x = 0 , x = 4$

#### Explanation:

$| x - 2 | + 10 = 12 \Rightarrow | x - 2 | = 12 - 10 = 2. \ldots \ldots \ldots \ldots . . \left(1\right)$

Recall that, $| y | = \pm y$

Hence, by $\left(1\right) , \pm \left(x - 2\right) = 2$

Case (1)
$+ \left(x - 2\right) = 2 \Rightarrow x = 4.$

Case (2)
$- \left(x - 2\right) = 2 \Rightarrow x - 2 = - 2 \Rightarrow x = 2 - 2 = 0.$

These satisfy the eqn.

Hence, the Solns. are $x = 0 , x = 4$