# How do you solve |x - 2| = 1?

Dec 21, 2016

The solution is $x = 3$ or $x = 1$

#### Explanation:

To clear the absolute-value bars, I must split the equation into its two possible two cases, one case for each sign:

$\left(x - 2\right) = 1 \text{ }$ or $\text{ } - \left(x - 2\right) = 1$

$x = 1 + 2 \text{ }$ or $\text{ } - x + 2 = 1$

$x = 3 \text{ " " }$ or $\text{ " " } x = 2 - 1 = 1$

Then the solutions are $x = 3$ or $x = 1$