# How do you solve abs(x-20<4?

May 31, 2015

Alternative Version of Question 1
$\left\mid x \right\mid - 20 < 4$
$\textcolor{w h i t e}{\text{XXXXX}}$$\left\mid x \right\mid < 24$
$\textcolor{w h i t e}{\text{XXXXX}}$$\rightarrow - 24 < x < 24$

Alternate Version of Question 2
$\left\mid x - 20 \right\mid < 4$
$\textcolor{w h i t e}{\text{XXXXX}}$Case 1: $\left(x - 20\right) < 0 \rightarrow x < 20$
$\textcolor{w h i t e}{\text{XXXXX}}$$\textcolor{w h i t e}{\text{XXXXX}}$$\left\mid x - 20 \right\mid < 4$
$\textcolor{w h i t e}{\text{XXXXX}}$$\textcolor{w h i t e}{\text{XXXXX}}$$20 - x < 4$
$\textcolor{w h i t e}{\text{XXXXX}}$$\textcolor{w h i t e}{\text{XXXXX}}$$x > 16$
$\textcolor{w h i t e}{\text{XXXXX}}$$16 < x < 20$

$\textcolor{w h i t e}{\text{XXXXX}}$Case2: $\left(x - 20\right) \ge 0 \rightarrow x \ge 20$
$\textcolor{w h i t e}{\text{XXXXX}}$$\textcolor{w h i t e}{\text{XXXXX}}$$\left\mid x - 20 \right\mid < 4$
$\textcolor{w h i t e}{\text{XXXXX}}$$\textcolor{w h i t e}{\text{XXXXX}}$$x - 20 < 4$
$\textcolor{w h i t e}{\text{XXXXX}}$$\textcolor{w h i t e}{\text{XXXXX}}$$x < 24$
$\textcolor{w h i t e}{\text{XXXXX}}$$20 \le x < 24$

Combining Case 1 and Case 2
$\textcolor{w h i t e}{\text{XXXXX}}$$16 < x < 24$