Question

Solve the inequality and graph the solution.
2(v+7)+1<11
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 \( 2(v + 7) + 1 < 11 \), we can follow these steps:

1. **Distribute**:
\[
2(v + 7) = 2v + 14
\]
The inequality now becomes:
\[
2v + 14 + 1 < 11
\]

2. **Combine like terms**:
\[
2v + 15 < 11
\]

3. **Isolate the variable**:
Subtract 15 from both sides:
\[
2v < 11 - 15
\]
\[
2v < -4
\]

4. **Divide by 2**:
\[
v < -2
\]

The solution to the inequality is \( v < -2 \).

### Graphing the Solution

1. **Endpoints**: The endpoint for this inequality is \( -2 \).

2. **Open or Closed**: Since the inequality is strictly less than (<), we will use an open circle at \( -2 \) to indicate that this endpoint is not included in the solution.

3. **Ray**: The solution is a ray extending to the left from \( -2 \), representing all values less than \( -2 \).

### Summary of the Graph

- Draw an open circle at \( -2 \).
- Shade the line to the left of \( -2 \) to indicate that all values less than \( -2 \) are included in the solution.

Here's a basic representation of the graph:

```
<----( -2 )---->
```

In this representation:
- The parentheses at \( -2 \) indicate that it is an open endpoint, meaning \( -2 \) is not part of the solution set. The arrow indicates that the shading extends infinitely left, representing all values less than \( -2 \).