Question

Solve for s and graph the solution.
3s–7≥5 or
s+19
4 open cirle or closed

≤5

Answer 1

To solve the inequality \( 3s - 7 \geq 5 \) or \( \frac{s + 19}{4} \leq 5 \), we'll tackle each part separately.

### First Inequality: \( 3s - 7 \geq 5 \)

1. Add 7 to both sides of the inequality:
\[
3s \geq 5 + 7
\]
\[
3s \geq 12
\]

2. Divide both sides by 3:
\[
s \geq 4
\]

### Second Inequality: \( \frac{s + 19}{4} \leq 5 \)

1. Multiply both sides by 4 (since we're multiplying by a positive number, the direction of the inequality remains unchanged):
\[
s + 19 \leq 20
\]

2. Subtract 19 from both sides:
\[
s \leq 1
\]

### Combined Solution

Now we combine the solutions from both inequalities:

- From the first inequality, we have \( s \geq 4 \).
- From the second inequality, we have \( s \leq 1 \).

Since the solution includes "or", we can state that:

- The complete solution is \( s \geq 4 \) or \( s \leq 1 \).

### Graphing the Solution

To graph the solution:

1. Draw a number line.
2. For \( s \geq 4 \):
- Place a closed circle at 4 (indicating that 4 is included).
- Shade the line to the right.

3. For \( s \leq 1 \):
- Place a closed circle at 1 (indicating that 1 is included).
- Shade the line to the left.

The graph should look like this:

```
<---|---|---|---|---|---|---|---|---|---|---|---|--->
-2 -1 0 1 2 3 4 5 6 7 8

●========================

●========================
```

Where:
- The line extending to the left from 1 indicates all values less than or equal to 1.
- The line extending to the right from 4 indicates all values greater than or equal to 4.