Question

Solve the inequality and graph the solution.
r/2 + 1 ≤ –1

Answer 1

To solve the inequality \( \frac{r}{2} + 1 \leq -1 \), we can follow these steps:

1. **Subtract 1 from both sides:**
\[
\frac{r}{2} + 1 - 1 \leq -1 - 1
\]
This simplifies to:
\[
\frac{r}{2} \leq -2
\]

2. **Multiply both sides by 2 to eliminate the fraction:**
\[
2 \cdot \frac{r}{2} \leq 2 \cdot -2
\]
This yields:
\[
r \leq -4
\]

The solution to the inequality is \( r \leq -4 \).

### Graphing the Solution
To graph the solution on a number line:

- Draw a number line with integers marked.
- Place a closed dot (or a filled circle) at \(-4\), indicating that \(-4\) is included in the solution set.
- Shade the region to the left of \(-4\) to show all values of \(r\) that satisfy \( r \leq -4\).

Here's how the number line looks:

```
<------●========|========|========|========|========|========|======>
-5 -4 -3 -2 -1 0 1
```

The shaded area includes all values to the left of \(-4\).