Question

Solve the inequality and graph the solution.
3>
m
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 \(3 > \frac{m}{2}\), we first need to manipulate the inequality to solve for \(m\).

Starting with:

\[
3 > \frac{m}{2}
\]

We can multiply both sides by 2 (since 2 is positive, the direction of the inequality remains the same):

\[
3 \cdot 2 > m
\]

\[
6 > m
\]

This can also be written as:

\[
m < 6
\]

Now we have the solution \(m < 6\).

### Graphing the Solution

1. **Plot the endpoint:** The endpoint in this case is \(m = 6\).
2. **Choose the type of endpoint:** Since the inequality is strict (less than), we will use an open circle at \(m = 6\) to indicate that 6 is not included in the solution.
3. **Shade the region:** Since \(m < 6\), we will shade everything to the left of 6 on the number line.

### Final Representation

The number line would look like this:

```
<----(6)-------------------
```
- The open circle at \(6\) indicates that \(6\) is not included in the solution.
- The shaded area to the left of \(6\) indicates all values of \(m\) that satisfy the inequality \(m < 6\).