# How do you graph and solve  | x - 2 | > 1?

May 19, 2017

$x < 1 \text{ and } x > 3$

#### Explanation:

Absolute value functions need to be broken into two functions:
$\left(x - 2\right) > 1 \text{ and } - \left(x - 2\right) > 1$

Solve for $x$:

$x - 2 + 2 > 1 + 2 \text{ and } - x + 2 > 1$

$x > 3 \text{ and } - x + 2 - 2 > 1 - 2$

$x > 3 \text{ and } - x > - 1$

Whenever you divide by a $- 1$ you need to switch the direction of the inequality.

$x > 3 \text{ and } - \frac{x}{-} 1 < - \frac{1}{-} 1$

$x > 3 \text{ and } x < 1$

When graphing use open holes or parentheses to show $< \mathmr{and} >$. Use a solid dot or a bracket to show $\le \mathmr{and} \ge$