Question

graph the compound inequality on the number line.

$x>1$ and $x\leq3$

Explanation:

Step1: Graph \(x > 1\)

For \(x>1\), we use an open - circle at \(x = 1\) (because \(x\) is not equal to \(1\)) and draw an arrow to the right.

Step2: Graph \(x\leq3\)

For \(x\leq3\), we use a closed - circle at \(x = 3\) (because \(x\) can be equal to \(3\)) and draw an arrow to the left.

Step3: Find the intersection

The compound inequality \(x>1\) and \(x\leq3\) means we take the overlapping part of the two graphs.

Answer:

On the number line, there is an open - circle at \(1\), a closed - circle at \(3\), and the line segment connecting these two points (including \(3\) and excluding \(1\)).