Chapter 4.9, Problem 4OE

To determine

To match: Inequality with the graph of its solution

Answer to Problem 4OE

The inequality matches with the given graph with option f.

Explanation of Solution

Given information:

The given equation is $\left(x+2\right)\left(x-3\right)\ge 0$

The equation can be simplified as:

  $\begin{array}{l}\left(x+2\right)\left(x-3\right)\ge 0\\ \text{Either both factors positive}\\ x+2\ge 0\text{ and }x-3\ge 0\\ x\ge -2\text{ and }x\ge 3\\ \text{or both factors negative}\\ x+2\le 0\text{ and }x-3\le 0\\ x\le -2\text{ and }x\le 3\end{array}$

The solution set of the given inequality is,

  $\left\{x:x\ge 3\text{ or }x\ge -2\right\}$

Therefore,

The inequality matches with the given graph with option f.