Question

which graph represents the compound inequality h≥5 and h<2

Explanation:

Step1: Analyze the inequality \(h\geq - 5\)

For \(h\geq - 5\), since the inequality is non - strict (\(\geq\)), we use a closed circle at \(h=-5\). The values of \(h\) that satisfy \(h\geq - 5\) are to the right of \(-5\) on the number line.

Step2: Analyze the inequality \(h < 2\)

For \(h < 2\), since the inequality is strict (\(<\)), we use an open circle at \(h = 2\). The values of \(h\) that satisfy \(h < 2\) are to the left of \(2\) on the number line.

Answer:

The graph with a closed circle at \(-5\) (because of \(h\geq - 5\)) and an open circle at \(2\) (because of \(h < 2\)) and the line segment connecting them (representing the values of \(h\) that satisfy both inequalities simultaneously) is the correct graph.