Question

Solve the inequality and graph the solution.
p+6<10
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 \( p + 6 < 10 \), we start by isolating \( p \):

1. Subtract 6 from both sides:

\[
p < 10 - 6
\]

\[
p < 4
\]

This means that \( p \) can take any value that is less than 4. The solution is \( p \in (-\infty, 4) \).

### Graphing the Solution

1. **Endpoints**: The endpoint here is \( 4 \). Since the inequality is strict (it does not include 4), we represent it as an open circle at 4 on the number line.

2. **Select an Endpoint to Change from Closed to Open**:
- We will use an open circle for the endpoint \( 4 \) (indicating that \( 4 \) is not included in the solution).

3. **Select the Middle of the Segment, Ray, or Line to Delete**:
- The interval \( (-\infty, 4) \) goes to the left from 4 towards negative infinity, and we will shade that part of the number line indicating that all values less than 4 are included in the solution.

### Final Representation

- The number line should look like this:

```
<---|----|----|----|----|----|----|----|----|----|----|----|---->
-2 -1 0 1 2 3 4 5 6
o
```

- The open circle at \( 4 \) indicates that it is not included, and the arrow to the left indicates that all numbers less than \( 4 \) are part of the solution set.

Thus, the solution to the inequality \( p + 6 < 10 \) is \( p < 4 \), and the graph represents this accurately.