Chapter 4.4, Problem 41AYU

To determine

To calculate:

The solution of following inequality equation:

  $\frac{3x-5}{x+2}\le 2$

Answer to Problem 41AYU

The solution of the inequality equation $\frac{3x-5}{x+2}\le 2$ is $x\le 9$ .

Explanation of Solution

Given information:

  $\frac{3x-5}{x+2}\le 2$

Calculation:

The given equation is:

  $\begin{array}{l}\frac{3x-5}{x+2}\le 2\\ \frac{3x-5}{x+2}-2\le 0\\ \frac{3x-5-2x-4}{x+2}\le 0\\ \frac{x-9}{x+2}\le 0\\ \frac{x-9}{x+2}=0\\ x-9=0OR\text{}x+2=0\\ x=9x=-2\end{array}$

The inequality value should be less than or equal to zero, from the above solution $-2<x\le 9$ .

Hence, the inequality is solved for $x\le 9$ .