Chapter A.9, Problem 74AYU

To determine

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

Answer to Problem 74AYU

$\left\{x|- \frac{2}{3} < x < 3\right\}$ or $\left(-\frac{2}{3,3}\right)$

Explanation of Solution

Given:

$0 < \frac{3x + 2}{2} < 4$

Calculation:

$0 < \frac{3x + 2}{2} < 4$

Multiply by 2

$0 < 3x + 2 < 8$

$0 - 2 < 3x + 2 - 2 < 8 - 2$

$- 2 < 3x < 6$

Divide by 3

$- \frac{2}{3} < x < 3$

The solution set is $\left\{x|- \frac{2}{3} < x < 3\right\}$ or using interval notation, all numbers in the interval $\left(-\frac{2}{3,3}\right)$