Question

Solve the inequality and graph the solution.
5n>10
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 \( 5n > 10 \), we can follow these steps:

1. **Divide both sides by 5**:
\[
n > \frac{10}{5}
\]
\[
n > 2
\]

2. **Identify the endpoint**: The inequality indicates that \( n \) can take any value greater than \( 2 \), but not equal to \( 2 \). So the endpoint is \( 2 \).

3. **Graph the solution**:
- Since the inequality is strict (greater than), we use an **open circle** at \( 2 \) to indicate that \( 2 \) is not included in the solution.
- Next, we shade or draw a ray to the right of \( 2 \) to indicate that all numbers greater than \( 2 \) are included.

Here’s how you would graph it:

- Draw a number line.
- Place an open circle at \( 2 \) to signify that \( 2 \) is not included.
- Shade or draw an arrow to the right of \( 2 \) indicating all values greater than \( 2 \).

The final solution is:
- The solution set is \( n > 2 \).
- Graphically represented as an open circle at \( 2 \) and a ray extending to the right: \( n \in (2, \infty) \).