Solve the inequality and graph the solution.

Question

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.