Question

Solve the inequality and graph the solution.
–
(n–3)>1
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 \( n - 3 > 1 \), we can follow these steps:

1. **Isolate \( n \)**:
\[
n - 3 > 1
\]
Add 3 to both sides:
\[
n > 1 + 3
\]
Simplifying the right side gives:
\[
n > 4
\]

2. **Graph the solution**:
The solution \( n > 4 \) means that \( n \) can take on any value greater than 4. To represent this graphically:

- We plot an open circle (indicating that 4 is not included) at the point \( n = 4 \).
- We then draw a ray or line extending to the right from the open circle to indicate all numbers greater than 4.

Here's the description of the plot:
- **Open Circle at 4**: This indicates that 4 is not included in the solution.
- **Ray extending right**: Indicating all values greater than 4.

If you visualize this on a number line, it looks like this:

```
<-----|-----|-----|-----|-----|-----|-----|----->
1 2 3 4 5 6 7
(=========>
```

Where:
- The parentheses \( ( \) around 4 indicate it's an open endpoint (not including 4).
- The arrow indicates all values greater than 4 are included in the solution.