Chapter A.9, Problem 86AYU

To determine

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

Answer to Problem 86AYU

$\left\{x|6 < x < \infty \right\}$ or $\left(6, \infty \right)$

Explanation of Solution

Given:

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

Calculation:

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

Multiply by $3x$

$0 < \frac{12x}{x} < \frac{6x}{3}$

$0 < 12 < 2x$

$2x > 12$

$\frac{2x}{2} > \frac{12}{2}$

$x > 6$

The solution set is $\left\{x|6 < x < \infty \right\}$ or using interval notation, all numbers in the interval $\left(6, \infty \right)$.