Question

which graph represents the compound inequality? h >= -5 and h < 2

Explanation:

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

On a number - line, \(h\geq - 5\) is represented by a closed - circle at \(-5\) (because the inequality includes equality) and an arrow pointing to the right.

Step2: Analyze \(h < 2\)

On a number - line, \(h < 2\) is represented by an open - circle at \(2\) (because the inequality does not include equality) and an arrow pointing to the left.

Step3: Find the intersection

The compound inequality \(h\geq - 5\) and \(h < 2\) means the values of \(h\) that satisfy both inequalities. The intersection is the set of numbers from \(-5\) (inclusive) to \(2\) (exclusive).

Answer:

The second graph (the one with a closed - circle at \(-5\), an open - circle at \(2\), and the line segment between them) represents the compound inequality \(h\geq - 5\) and \(h < 2\).