Chapter A.9, Problem 81AYU

To determine

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

Answer to Problem 81AYU

$\left\{x|\frac{1}{2} \le x < \frac{5}{4}\right\}$ or $\left[\frac{\frac{1}{2,5}}{4}\right)$

Explanation of Solution

Given:

$\frac{1}{2} \le \frac{x + 1}{3} < \frac{3}{4}$

Calculation:

$\frac{1}{2} \le \frac{x + 1}{3} < \frac{3}{4}$

$\frac{1}{2} - \frac{1}{3} \le \frac{x + 1}{3} - \frac{1}{3} < \frac{3}{4} - \frac{1}{3}$   -----(Subtract $\frac{1}{3}$)

$\frac{1}{6} \le \frac{x}{3} < \frac{5}{12}$

$\frac{3}{6} \le x < \frac{15}{12}$   -----(Multiply 3)

$\frac{1}{2} \le x < \frac{5}{4}$

The solution set is $\left\{x|\frac{1}{2} \le x < \frac{5}{4}\right\}$ or using interval notation, all numbers in the interval $\left[\frac{\frac{1}{2,5}}{4}\right)$.