Question

graph the compound inequality on the number line.
x>5 and x≤7

Explanation:

Step1: Graph \( x > 5 \)

For \( x>5 \), we use an open - circle at \( x = 5 \) (because \( 5\) is not included in the solution set) and draw an arrow to the right.

Step2: Graph \( x\leq7 \)

For \( x\leq7 \), we use a closed - circle at \( x = 7 \) (because \( 7\) is included in the solution set) and draw an arrow to the left.

Step3: Find the intersection

The compound inequality \( x>5\) and \(x\leq7\) means we take the overlapping part of the two graphs. So we have an open - circle at \(5\), a closed - circle at \(7\), and the line segment connecting them.

Answer:

On the number line, place an open circle at \(5\), a closed circle at \(7\), and draw a line segment connecting these two points.