Chapter 6.5, Problem 46MR

To determine

To write: The compound inequality representing given phrase and to graph the solutions.

Explanation of Solution

Given information:

The given phrase is “All real numbers that are greater than $2$ and less than or equal to $7$ ”

Calculation:

Let x is the set of all real numbers.

The given phrase is represented as $x>2\text{ and }x\le 7$

  $\Rightarrow \text{2}<x\le 7$

Graph:

The graph of the $\text{2}<x\le 7$ is shown below

  

The shaded region is the solution of the inequality.

Hence, the compound inequality representing given phrase is $\text{2}<x\le 7.$