Question

graph the compound inequality on the number line. x>2 and x≤5

Explanation:

Step1: Mark the boundary points

Mark 2 and 5 on the number - line.

Step2: Represent \(x>2\)

Since \(x > 2\), use an open circle at \(x = 2\) to indicate that 2 is not included in the solution set, and draw an arrow to the right.

Step3: Represent \(x\leq5\)

Since \(x\leq5\), use a closed circle at \(x = 5\) to indicate that 5 is included in the solution set, and draw an arrow to the left from 5. The overlapping part of the two arrows is the solution of the compound - inequality.

Answer:

On the number - line, there is an open circle at 2, a closed circle at 5, and the line segment between 2 and 5 (including 5 but not 2) is shaded.