Question

or
Solve the inequality and graph the solution.
p+2
2
≤
–
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

\[
\frac{p + 2}{2} \leq -1,
\]

we first start by multiplying both sides by 2 to eliminate the fraction:

\[
p + 2 \leq -2.
\]

Next, we isolate \(p\) by subtracting 2 from both sides:

\[
p \leq -2 - 2,
\]

which simplifies to:

\[
p \leq -4.
\]

Now, let's represent \(p \leq -4\) on a number line.

1. **Identifying Endpoints**: The endpoint in this case is \(-4\).
2. **Closed/Open Endpoint**: Since the inequality is less than or equal to (\(\leq\)), we will use a closed dot at \(-4\) to indicate that this point is included in the solution set.
3. **Graphing the solution**: The solution includes all numbers less than or equal to \(-4\).

### Number Line Graph:

- Mark \(-4\) with a closed dot.
- Shade to the left of \(-4\) to indicate all numbers less than \(-4\).

Here's a textual representation:

```
<---●============================>
-4
```

In summary, the solution to the inequality is \(p \leq -4\), represented on the number line with a closed dot at \(-4\) and shading to the left.