Question

graph the compound inequality.
x > -20 and x ≤ -10
plot the endpoints. select an endpoint to change it from closed to open. s
a segment, ray, or line to delete it.

Explanation:

Step1: Analyze the inequality \(x > - 20\)

For \(x > - 20\), we use an open circle at \(x=-20\) (because \(-20\) is not included in the solution set) and draw a ray to the right.

Step2: Analyze the inequality \(x\leq - 10\)

For \(x\leq - 10\), we use a closed circle at \(x = - 10\) (because \(-10\) is included in the solution set) and draw a ray to the left.

Step3: Find the intersection

The compound - inequality \(x > - 20\) and \(x\leq - 10\) means we take the overlapping part of the two graphs. The overlapping part is the segment from an open circle at \(x=-20\) to a closed circle at \(x = - 10\).

Answer:

On the number - line, there is an open circle at \(-20\) and a closed circle at \(-10\), and the segment between them is shaded.