Question

Solve the inequality and graph the solution.
16(g+5)–20≥12
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 \( 16(g + 5) - 20 \geq 12 \), we'll first simplify the left side.

1. Distribute \( 16 \):
\[
16g + 80 - 20 \geq 12
\]

2. Combine like terms:
\[
16g + 60 \geq 12
\]

3. Subtract \( 60 \) from both sides to isolate the variable term:
\[
16g \geq 12 - 60
\]
\[
16g \geq -48
\]

4. Divide both sides by \( 16 \):
\[
g \geq \frac{-48}{16}
\]
\[
g \geq -3
\]

Now we have the solution \( g \geq -3 \).

### Graphing the Solution

1. The endpoint of the solution is at \( g = -3 \).
2. Since the inequality is \( g \geq -3 \), the endpoint at \( g = -3 \) is included in the solution, so we will use a closed dot at \( -3 \).
3. The solution includes all values greater than \(-3\), extending to infinity.

### Graph Representation

- **Mark the point \( -3 \)** with a closed dot.
- **Draw a ray** starting from \( -3 \) and extending to the right (towards positive infinity).

### Final Representation:
- Closed dot at \( -3 \) (indicating it is included).
- Arrow extending to the right from \( -3 \) indicating all values greater than \(-3\) are included in the solution.

In summary, the inequality \( g \geq -3 \) signifies all values of \( g \) that are equal to or greater than \( -3 \).