Question

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

Explanation:

Step1: Analyze the first inequality

For $h\geq - 5$, there is a closed - circle at $h=-5$ (because the inequality includes equality) and the line extends to the right.

Step2: Analyze the second inequality

For $h < 2$, there is an open - circle at $h = 2$ (because the inequality does not include equality) and the line extends to the left.

Step3: Combine the two inequalities

The solution of the compound inequality $h\geq - 5$ and $h < 2$ is the intersection of the two solution sets, which is the interval from $-5$ (closed - circle) to $2$ (open - circle).

Answer:

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