Solve the inequality and graph the solution.

Question

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.