Question

Solve the inequality and graph the solution.
4(v+1)<12
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 \( 4(v + 1) < 12 \), we first simplify it:

1. Distribute \( 4 \) on the left side:
\[
4v + 4 < 12
\]

2. Subtract \( 4 \) from both sides:
\[
4v < 8
\]

3. Divide both sides by \( 4 \):
\[
v < 2
\]

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

### Graphing the Solution

1. **Plot the Endpoint**: The endpoint is \( 2 \).
2. **Select the Nature of the Endpoint**: Since \( v < 2 \) (not \( \leq 2 \)), we use an open circle at \( 2 \).
3. **Graphing the Ray**: Since \( v < 2 \), we shade to the left of the open circle to represent all values less than \( 2 \).

#### Final Representation
- The graph will have an open circle at \( 2 \), and a shaded line extending to the left. The left side of the graph continues indefinitely.

### Summary
- Solution: \( v < 2 \)
- Graph: Open circle at \( 2 \) with shading to the left.