Question

which graph represents the solutions to this inequality?
2h + 5 > 31 and -3h - 12 ≥ -75

Explanation:

Step1: Solve the first inequality

Solve \(2h + 5>31\).
Subtract \(5\) from both sides: \(2h>31 - 5\), so \(2h>26\).
Divide both sides by \(2\): \(h > 13\).

Step2: Solve the second inequality

Solve \(-3h-12\geq - 75\).
Add \(12\) to both sides: \(-3h\geq-75 + 12\), so \(-3h\geq-63\).
Divide both sides by \(-3\) (and reverse the inequality sign): \(h\leq21\).

Answer:

The solution of the compound - inequality \(13 < h\leq21\) is represented by the second graph (where there is an open circle at \(13\) and a closed circle at \(21\) and the line segment between them).