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 $m<6$.