Question

Solve the inequality and graph the solution.
1>f–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 \( 1 > f - 7 \), we can first rearrange it:

\[
1 + 7 > f
\]
\[
8 > f
\]
or alternatively,
\[
f < 8
\]

This means that \( f \) can take any value less than 8.

### Graphing the Solution

1. **Endpoints**: The endpoint of our solution is \( f = 8 \).
2. **Closed or Open**: Since \( f \) must be less than 8 and not equal to it, we use an open circle at \( f = 8 \) to indicate that 8 is not included in the solution.
3. **Deleting the middle**: Since \( f < 8 \) means all numbers less than 8, we will graph this on a number line.

### Graph Representation:

- Draw a number line.
- Place an open circle at \( 8 \) to show that it's not included.
- Shade to the left of \( 8 \) to represent all values less than 8.

```
<---o=========================>
8
```

Here, "o" indicates an open circle at \( 8 \) and the line shaded to the left shows all numbers that satisfy the inequality \( f < 8 \).