Chapter 4.4, Problem 43AYU

To determine

To calculate:

The solution of the following inequality equation:

  $\frac{1}{x-2}<\frac{2}{3x-9}$

Answer to Problem 43AYU

The solution of the inequality equation $\frac{1}{x-2}<\frac{2}{3x-9}$ is $x<2,3<x<5$ .

Explanation of Solution

Given information:

  $\frac{1}{x-2}<\frac{2}{3x-9}$

Calculation:

The given equation is:

  $\begin{array}{l}\frac{1}{x-2}<\frac{2}{3x-9}\\ \frac{1}{x-2}-\frac{2}{3x-9}<0\\ \frac{3x-9-2x+4}{\left(x-2\right)\left(3x-9\right)}<0\\ \frac{3x-9-2x+4}{\left(x-2\right)\left(3x-9\right)}<0\\ \frac{x-5}{\left(x-2\right)\left(3x-9\right)}<0\\ x-5=0OR\text{}x-2=0OR3x-9=0\\ x=5x=2x=3\\ \end{array}$

Hence, the inequality is solved for $x<2,3<x<5$ .