Question

Solve the inequality and graph the solution.
v
4
<
–
2
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 \( \frac{v}{4} < -2 \), we start by isolating \( v \).

1. Multiply both sides of the inequality by 4 (since 4 is positive, the direction of the inequality remains the same):
\[
v < -2 \times 4
\]
\[
v < -8
\]

The solution to the inequality is \( v < -8 \).

### Graphing the Solution

1. **Endpoints**: The endpoint here is -8.
2. **Type of Endpoint**: Since the inequality is strict (i.e., it does not include -8), we will use an open circle to represent -8 on the graph.
3. **Deleting the segment**: We want to shade to the left of -8, indicating all values less than -8.

### Graph Representation

- Draw a number line.
- Place an open circle at -8.
- Shade all numbers to the left of -8 to represent \( v < -8 \).

Here's a rough representation of the graph:

```
<---O========================
-8
```

The open circle signifies that -8 is not included in the solution. The shaded area to the left of -8 represents all values less than -8.