# How do you solve abs(2x-3)>1?

Oct 7, 2015

$x < 1 \text{ or } x > 2$

#### Explanation:

If $x \ge \frac{3}{2}$
then $\left\mid 2 x - 3 \right\mid = 2 x - 3$
$\textcolor{w h i t e}{\text{XX}} \left\mid 2 x - 3 \right\mid > 1$
$\textcolor{w h i t e}{\text{XX}} \rightarrow 2 x - 3 > 1$
$\textcolor{w h i t e}{\text{XX}} \rightarrow 2 x > 4$
$\textcolor{w h i t e}{\text{XX}} \rightarrow x > 2$

If $x < \frac{3}{2}$
then $\left\mid 2 x - 3 \right\mid = 3 - 2 x$
$\textcolor{w h i t e}{\text{XX}} \left\mid 2 x - 3 \right\mid > 1$
$\textcolor{w h i t e}{\text{XX}} \rightarrow 3 - 2 x > 1$
$\textcolor{w h i t e}{\text{XX}} \rightarrow 3 > 2 x + 1$
$\textcolor{w h i t e}{\text{XX}} \rightarrow 1 > 2 x$
$\textcolor{w h i t e}{\text{XX}} \rightarrow 1 > x$

Combining the two case we get
color(white)("XX")x < 1 " or " x > 2