Question

Solve the inequality and graph the solution.
–
12<4(s–1)
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 \(-12 < 4(s - 1)\), we'll follow these steps:

1. Distribute the \(4\) on the right side:
\[
-12 < 4s - 4
\]

2. Add \(4\) to both sides of the inequality:
\[
-12 + 4 < 4s
\]
\[
-8 < 4s
\]

3. Divide both sides by \(4\):
\[
-2 < s
\]
This can also be rewritten as:
\[
s > -2
\]

Now, let's express the solution set in interval notation:
- The solution is \(s \in (-2, \infty)\).

### Graphing the solution:
1. **Endpoints**: The endpoint is \(-2\). Since \(s > -2\), we will make this endpoint **open** (not included).

2. **Graph**:
- Draw a number line.
- Place an open circle at \(-2\).
- Shade to the right of \(-2\) extending to infinity.

### Visual Representation:
Here's how you would represent it visually, though I cannot draw directly:

```
<---(-2)========>
```
- The paranthesis \(()\) around \(-2\) indicates that it is an open endpoint, meaning \(-2\) is not included in the solution set.
- The shading to the right indicates that all values greater than \(-2\) are included in the solution.