# How do you solve abs(x-1)>2?

Oct 31, 2016

$x > 3$ or $x < - 1$

#### Explanation:

$\left\mid x - 1 \right\mid > 2$

This absolute value inequality can be rewritten as two inequalities.

$x - 1 > 2 \textcolor{w h i t e}{a a a}$ or$\textcolor{w h i t e}{a a} x - 1 < - 2$

Add $1$ to both sides.

$x - 1 > 2 \textcolor{w h i t e}{a a a a a a a} x - 1 < - 2$
$\textcolor{w h i t e}{a} + 1 \textcolor{w h i t e}{a} + 1 \textcolor{w h i t e}{a {a}^{2} a a a a a} + 1 \textcolor{w h i t e}{a {a}^{2}} + 1$

$x > 3 \textcolor{w h i t e}{a a a a a a} \mathmr{and} \textcolor{w h i t e}{a a a a a} x < - 1$