Solve the inequality and graph the solution.

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 \(-4\).