Question

Solve the inequality and graph the solution.
3>
v
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 \( 3 > \frac{v}{2} \), we can first rewrite it in a more standard form:

1. Multiply both sides of the inequality by \( 2 \) (since \( 2 \) is positive, this does not change the direction of the inequality):

\[
3 \times 2 > v
\]

This simplifies to:

\[
6 > v
\]

or

\[
v < 6
\]

This tells us the solution set is all values of \( v \) that are less than \( 6 \).

### Graphing the Solution

1. **Endpoints**: The endpoint here is \( 6 \).
2. **Open or Closed**: Since the inequality does not include \( 6 \) (as indicated by the \( < \) symbol), we mark this point as an open endpoint.

3. **Noting the direction**: Since \( v < 6 \), we will shade all the values to the left of \( 6 \) on a number line.

### Graph Representation
- The number line will have an open circle at \( 6 \).
- Shade everything to the left of \( 6 \) to represent all values of \( v \) less than \( 6 \).

### Final Representation
It will look like this:

```
<---(--------------------)------------------->
0 6
```

In summary:
- The solution to the inequality is \( v < 6 \).
- Graphically, it is represented by an open circle at \( 6 \) with shading to the left.