Question

Solve the inequality and graph the solution.
2(g–1)≥6
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 \( 2(g - 1) \geq 6 \), follow these steps:

1. **Distribute the 2**:
\[
2g - 2 \geq 6
\]

2. **Add 2 to both sides**:
\[
2g \geq 8
\]

3. **Divide both sides by 2**:
\[
g \geq 4
\]

So the solution to the inequality is \( g \geq 4 \).

### Graphing the solution:

1. **Endpoints**: The endpoint for \( g = 4 \) is included (since the inequality is greater than or equal to), so we plot this as a closed point at \( g = 4 \).

2. **Ray**: The solution also indicates that all values greater than 4 are part of the solution. We will represent this as a ray extending to the right from the point \( g = 4 \).

### Final Graphic Representation:

- Plot a closed dot at \( g = 4 \) (indicating that 4 is included in the solution).
- Draw a ray extending to the right from this point, representing all values greater than 4.

### Summary of the Graph:
- Closed dot on \( g = 4 \).
- Ray extending to the right (toward infinity).

This completes the solution of the inequality \( 2(g - 1) \geq 6 \).