Question

Solve the inequality and graph the solution. 2(s–1)≥6 Plot the endpoints.

Answer 1

To solve the inequality \( 2(s - 1) \geq 6 \), we can follow these steps:

1. **Distribute the 2**:
\[
2s - 2 \geq 6
\]

2. **Add 2 to both sides**:
\[
2s \geq 6 + 2
\]
\[
2s \geq 8
\]

3. **Divide both sides by 2**:
\[
s \geq \frac{8}{2}
\]
\[
s \geq 4
\]

The solution to the inequality is \( s \geq 4 \).

### Graphing the Solution

1. **Endpoint**: The endpoint of the solution is 4.
2. Since the inequality includes "greater than or equal to" (≥), we plot a solid circle (or closed dot) at 4 to indicate that 4 is included in the solution set.
3. Draw a line or arrow extending to the right from the point 4 to indicate that all values greater than 4 are included in the solution.

Here’s how it looks:

```
<---(---------]---------------->
4
```

- The solid dot at 4 signifies that 4 is part of the solution (since \( s \) can be equal to 4).
- The arrow on the right means all numbers greater than 4 are included in the solution set.