Solve the inequality and graph the solution.

Question

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 \(m < 6\).