Chapter 4.4, Problem 42AYU

To determine

To calculate:

The solution of the following inequality equation:

  $\frac{x-4}{2x+4}\ge 1$

Answer to Problem 42AYU

The solution of the inequality equation $\frac{x-4}{2x+4}\ge 1$ is $-8<x\le -2$ .

Explanation of Solution

Given information:

  $\frac{x-4}{2x+4}\ge 1$

Calculation:

The given equation is:

  $\begin{array}{l}\frac{x-4}{2x+4}\ge 1\\ \frac{x-4}{2x+4}-1\ge 0\\ \frac{x-4-2x-4}{2x+4}\ge 0\\ \frac{-x-8}{2x+4}\ge 0\\ \frac{-x-8}{2x+4}=0\\ -x-8=0OR\text{}2x+4=0\\ x=-8x=-2\end{array}$

The inequality value should be less than or equal to zero, from the above solution $x=-8,x=-2$ .

Hence, the inequality is solved for $-8<x\le -2$ .