Chapter A.9, Problem 96AYU

To determine

To solve: Each inequality. Express your answer using set notation or interval notation. Graph the solution set.

Answer to Problem 96AYU

$\left\{x|x < \frac{1}{3} or x > 1\right\}$ or $\left(-\infty , \frac{1}{3}\right) \cup \left(1, \infty \right)$

Explanation of Solution

$\left|2 - 3x\right| > 1$

$2 - 3x < - 1$ or $2 - 3x > 1$

$2 - 3x - 2 < - 1 - 2$ or $2 - 3x - 2 > 1 - 2$

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

Divide by $- 3$

$x > 1$ or $x < \frac{1}{3}$

The solution set is $\left\{x|x < \frac{1}{3} or x > 1\right\}$ or using interval notation, all numbers in the interval $\left(-\infty , \frac{1}{3}\right) \cup \left(1, \infty \right)$.