Question

Solve the inequality and graph the solution.
s–2
3
≥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

\[
\frac{s - 2}{3} \geq 2,
\]

we will first eliminate the fraction by multiplying both sides by 3:

\[
s - 2 \geq 6.
\]

Next, we isolate \(s\) by adding 2 to both sides:

\[
s \geq 8.
\]

This means that the solution to the inequality is:

\[
s \in [8, \infty).
\]

To graph the solution, we can follow these steps:

1. **Mark the Endpoint**: Place a closed circle (or dot) on the number 8 to indicate that 8 is included in the solution set.
2. **Draw the Ray**: Shade to the right from point 8 to represent all values greater than 8.

In the given request to "select an endpoint to change it from closed to open," we'll convert the closed endpoint at \(8\) to an open endpoint. So, we would use an open circle on 8.

3. **Adjusting the Graph**:
- Change the closed circle at \(8\) to an open circle.
- The graph will then be an open circle at \(8\) with a ray extending to the right.

The desired graph can be shown as:

\[
\text{Open circle at 8} \quad \text{and a ray extending right: } (8, \infty)
\]

In summary:
- **Solution**: \(s \in (8, \infty)\)
- **Graph**: Open circle at \(8\) and a ray extending to the right towards positive infinity.