Question

Solve for s and graph the solution. 3s–7≥5 or s+19 4 ≤5 Plot the endpoints.

Answer 1

To solve the compound inequality \(3s - 7 \geq 5\) or \(s + 19 \leq 5\), we will solve each inequality separately.

### First Inequality:
1. **Solve** \(3s - 7 \geq 5\):
\[
3s - 7 + 7 \geq 5 + 7
\]
\[
3s \geq 12
\]
\[
s \geq \frac{12}{3}
\]
\[
s \geq 4
\]

### Second Inequality:
2. **Solve** \(s + 19 \leq 5\):
\[
s + 19 - 19 \leq 5 - 19
\]
\[
s \leq -14
\]

### Combining the Solutions:
The solutions for the inequalities are \(s \geq 4\) and \(s \leq -14\). Since we have an "or" condition, either of these solutions satisfies the original problem.

### Summary of Solutions:
- \(s \geq 4\) (includes all values of \(s\) from 4 to infinity)
- \(s \leq -14\) (includes all values of \(s\) from negative infinity to -14)

### Graphing the Solutions:
- For \(s \geq 4\): Draw a solid circle at 4 and shade to the right.
- For \(s \leq -14\): Draw a solid circle at -14 and shade to the left.

### Visual Representation:
```
<--(====================) 4
(-14)====================>
```
The left and right areas shaded represent the solution sets for \(s \leq -14\) and \(s \geq 4\) respectively, while the solid circles indicate that those points (the endpoints) are included in the solution.