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
- Plot the endpoint: The endpoint in this case is \(m = 6\).
- 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.
- 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 \(m < 6\).