Question

Solve the inequality and graph the solution.
8<3(v–2)–4
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 \( 8 < 3(v - 2) - 4 \), we first simplify the right-hand side:

1. Distribute the \( 3 \):
\[
3(v - 2) = 3v - 6
\]
So the inequality becomes:
\[
8 < 3v - 6 - 4
\]

2. Combine like terms on the right:
\[
3v - 6 - 4 = 3v - 10
\]
Therefore, the inequality is:
\[
8 < 3v - 10
\]

3. Add \( 10 \) to both sides to isolate the term with \( v \):
\[
8 + 10 < 3v
\]
This simplifies to:
\[
18 < 3v
\]

4. Divide both sides by \( 3 \) to solve for \( v \):
\[
\frac{18}{3} < v
\]
Which simplifies to:
\[
6 < v
\]
or in standard form:
\[
v > 6
\]

### Graphing the Solution

1. **Plotting the endpoints**: The solution is \( v > 6 \). We’ll plot the point \( 6 \).

2. **Closed vs. Open endpoints**: Since the inequality is strictly greater than (not including \( 6 \)), we make the endpoint \( 6 \) open.

3. **Graphing the ray**: The graph will show all values of \( v \) to the right of \( 6 \):
- Use an open circle at \( 6 \) to indicate that \( 6 \) is not included in the solution.
- Shade the region to the right of \( 6 \) to represent all numbers greater than \( 6 \).

### Final Result

The solution to the inequality is \( v > 6 \), and the graph will look like this:

- An open circle at \( 6 \).
- A line extending to the right (toward positive infinity).

\[
\text{Graph:}
\]
\[
\text{(Open circle at 6, shading to the right)}
\]