Question

graph the compound inequality. x > 5 and x ≤ 9 plot the endpoints. select an endpoint to change it from closed to open. select the middle of a segment, ray, or line to delete it.

Explanation:

Step1: Identify the inequality types

The first inequality $x > 5$ is a strict - inequality, so 5 is not included. The second inequality $x\leq9$ is a non - strict inequality, so 9 is included.

Step2: Plot the endpoints on the number line

For $x > 5$, we use an open circle at 5 to indicate that 5 is not part of the solution set. For $x\leq9$, we use a closed circle at 9 to indicate that 9 is part of the solution set.

Step3: Shade the solution region

We shade the region between 5 and 9 on the number line, including 9 but not including 5.

Answer:

On the given number line, place an open circle at 5 and a closed circle at 9, then shade the region between them.