Question

solve the inequality and graph the solution.
3 ≥ -6(h + 2) - 9
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.

Explanation:

Step1: Expand the inequality

Start with the inequality \( 3 \geq -6(h + 2) - 9 \). First, expand the right - hand side:
\(-6(h + 2)-9=-6h-12 - 9=-6h-21\)
So the inequality becomes \( 3\geq - 6h-21\).

Step2: Add 21 to both sides

Add 21 to each side of the inequality to isolate the term with \(h\).
\(3 + 21\geq-6h-21 + 21\)
\(24\geq - 6h\)

Step3: Divide both sides by - 6 (and reverse the inequality)

When dividing an inequality by a negative number, the direction of the inequality sign changes. Divide both sides by - 6:
\(\frac{24}{-6}\leq\frac{-6h}{-6}\)
\(- 4\leq h\) or \(h\geq - 4\)

Answer:

The solution to the inequality is \(h\geq - 4\). To graph this, we use a closed circle at \(h=-4\) (because the inequality is "greater than or equal to") and draw a ray to the right of \(-4\) on the number line.