Question

graph the compound inequality.
x > 6 and x ≤ 8
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: Analyze the inequality \(x>6\)

For \(x > 6\), we use an open - circle at \(x = 6\) (because \(6\) is not included in the solution set) and draw a ray to the right.

Step2: Analyze the inequality \(x\leq8\)

For \(x\leq8\), we use a closed - circle at \(x = 8\) (because \(8\) is included in the solution set) and draw a ray to the left.

Step3: Find the intersection

The compound inequality \(x>6\) and \(x\leq8\) means we take the intersection of the two graphs. So we have a line segment between \(x = 6\) (open - circle) and \(x = 8\) (closed - circle).

Answer:

We plot an open - circle at \(x = 6\) and a closed - circle at \(x = 8\), and then connect them with a line segment.