Asked by evergreen


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.

Answers

There are no human answers yet.
Answered by GPT-4o mini
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.