# How do you graph and solve |x – 1| ≥ 2 ?

Nov 25, 2015

One way is to consider the two cases for the absolute value separately.
Since this is a relationship in one variable it can be graphed on a number line as:

#### Explanation:

Case 1: $\textcolor{b l a c k}{\left(x - 1\right) \ge 0}$
$\textcolor{w h i t e}{\text{XXX}} \left\mid x - 1 \right\mid \ge 2$

$\textcolor{w h i t e}{\text{XXX}} x - 1 \ge 2$

$\textcolor{w h i t e}{\text{XXX}} x \ge 3$

Case 2: $\textcolor{b l a c k}{x - 1} < 0$
$\textcolor{w h i t e}{\text{XXX}} \left\mid x - 1 \right\mid \ge 2$

$\textcolor{w h i t e}{\text{XXX}} 1 - x \ge 2$

$\textcolor{w h i t e}{\text{XXX}} - 1 \ge x$