Question

graph the compound inequality.
x > 72 and x < 76
plot the endpoints. select an endpoint to change it from closed to open. select the middle a segment, ray, or line to delete it.

Explanation:

Step1: Analyze the inequality symbols

For \(x > 72\), since the symbol is \(>\), the endpoint at \(x = 72\) is open. For \(x < 76\), since the symbol is \(<\), the endpoint at \(x = 76\) is open.

Step2: Determine the interval

The compound inequality \(x>72\) and \(x < 76\) represents all real numbers \(x\) such that \(x\) is greater than \(72\) and less than \(76\). On the number - line, we shade the region between \(72\) and \(76\).

Answer:

On the number - line, place an open circle at \(x = 72\) (because \(x
eq72\) as \(x>72\)) and an open circle at \(x = 76\) (because \(x
eq76\) as \(x < 76\)), then shade the line segment between \(72\) and \(76\).