Question

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

Explanation:

Step1: Solve the first inequality $2h + 5>31$

Subtract 5 from both sides: $2h>31 - 5$, so $2h>26$. Then divide both sides by 2: $h > 13$.

Step2: Solve the second - inequality $-3h-12\geq - 75$

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 is $13 < h\leq21$. The graph with an open circle at 13 and a closed circle at 21 with a line segment between them represents the solution.