Chapter A.9, Problem 71AYU

To determine

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

Answer to Problem 71AYU

$\left\{x|1 \le x \le 4\right\}$ or $\left[\frac{2}{3}, 3\right]$

Explanation of Solution

Given:

$- 5 \le 4 - 3x \le 2$

Calculation:

$- 5 \le 4 - 3x \le 2$

$- 5 - 4 \le 4 - 3x - 4 \le 2 - 4$   -----(Subtract $4$)

$- 9 \le - 3x \le -2$

$\frac{- 9}{- 3} \ge \frac{- 3x}{- 3} \ge \frac{- 2}{- 3}$   -----(Divide $-3$)

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

The solution set is $\left\{x|\frac{2}{3} \le x \le 3\right\}$ or using interval notation, all numbers in the interval $\left[\frac{2}{3}, 3\right]$