Solve the inequality and graph the solution.

Question

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.

Answer 1

To solve the inequality \(3 \geq -6(h + 2) - 9\), we will first simplify and solve for \(h\).

1. Distribute the \(-6\): \[ 3 \geq -6h - 12 - 9 \]

2. Combine like terms on the right side: \[ 3 \geq -6h - 21 \]

3. Add 21 to both sides to isolate the term with \(h\): \[ 3 + 21 \geq -6h \] \[ 24 \geq -6h \]

4. Divide both sides by \(-6\). Remember that since we are dividing by a negative number, we must flip the inequality: \[ \frac{24}{-6} \leq h \] \[ -4 \leq h \]

Thus, the solution to the inequality is: \[ h \geq -4 \]

Graphing the Solution

• Plot the endpoint at \(h = -4\). Since \(h\) can equal \(-4\), we will use a closed circle at \(-4\).
• The inequality \(h \geq -4\) means that \(h\) can take any value greater than \(-4\), so we will draw a line extending to the right from the closed circle at \(-4\).

Final representation:

• Closed circle at \(-4\) (indicating that \(-4\) is included).
• Arrow extending to the right (indicating that all values greater than \(-4\) are included).

If you need to delete a segment or ray in the middle, let me know how you'd like to modify the graph further!