Question

Solve the inequality and graph the solution.
–
9<3(g–7)
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 \(-9 < 3(g - 7)\), follow these steps:

1. **Distribute the 3**:
\[
-9 < 3g - 21
\]

2. **Add 21 to both sides**:
\[
-9 + 21 < 3g
\]
\[
12 < 3g
\]

3. **Divide both sides by 3**:
\[
\frac{12}{3} < g
\]
\[
4 < g
\]
This can also be written as:
\[
g > 4
\]

### Graphing the solution:

To graph \(g > 4\):

- **Endpoint at 4**: Use an open circle at 4 to indicate that 4 is not included in the solution.
- **Shade to the right**: This shows that all values greater than 4 are included in the solution.

### Summary of the graph:

- The point at \(g = 4\) is an open circle.
- Shade the region to the right of the point to indicate all values greater than 4.

The final graph looks like this:

```
<---o-------------------->
4
```

Where the open circle at 4 indicates that the value is not included in the solution.