Chapter A.9, Problem 85AYU

To determine

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

Answer to Problem 85AYU

$\left\{x|\frac{10}{3} < x < \infty \right\}$ or $\left(\frac{10}{3}, \infty \right)$

Explanation of Solution

Given:

$0 < \frac{2}{x} < \frac{3}{5}$

Calculation:

$0 < \frac{2}{x} < \frac{3}{5}$

Multiply by $5x$

$0 < \frac{10x}{x} < \frac{15x}{5}$

$0 < 10 < 3x$

$3x > 10$

$\frac{3x}{3} > \frac{10}{3}$   -----(Divide 3)

$x > \frac{10}{3}$

The solution set is $\left\{x|\frac{10}{3} < x < \infty \right\}$ or using interval notation, all numbers in the interval $\left(\frac{10}{3}, \infty \right)$.