# How do you solve and graph the solution set of |2x-1|<=2?

Nov 8, 2016

The solution of the inequality is $- 0.5 \le x \le 1.5$.

#### Explanation:

When solving an absolute value inequality, the process used actually depends upon which inequality symbol is in the original inequality. If the inequality symbol is $<$ or $\le$, solve using an "and" compound inequality. If the inequality symbol is $>$ or $\ge$, solve using an "or" compound inequality. Since this inequality has a $\le$ symbol, it will be solved using an "and" compound inequality.

$| 2 x - 1 | \le 2$

$- 2 \le 2 x - 1 \le 2$

$- 2 + 1 \le 2 x - 1 + 1 \le 2 + 1$

$- 1 \le 2 x \le 3$

$\frac{- 1}{2} \le \frac{2 x}{2} \le \frac{3}{2}$

$- 0.5 \le x \le 1.5$

To graph this solution, put closed dots at $- 0.5$ and $1.5$ and shade the number line between the dots.