Question

graph the compound inequality on the number line. x < -2 and x > -8

Explanation:

Step1: Identify the lower - bound

The lower - bound of the compound inequality is \(x>-8\). On the number line, we use an open circle at \(-8\) (since \(x\) is strictly greater than \(-8\)) and shade to the right of \(-8\).

Step2: Identify the upper - bound

The upper - bound of the compound inequality is \(x < - 2\). On the number line, we use an open circle at \(-2\) (since \(x\) is strictly less than \(-2\)) and shade to the left of \(-2\).

Step3: Find the intersection

The solution of the compound inequality \(x < - 2\) and \(x>-8\) is the intersection of the two shaded regions. So we shade the region between \(-8\) and \(-2\) with open circles at \(-8\) and \(-2\).

Answer:

On the number line, place open circles at \(-8\) and \(-2\) and shade the region between them.