or

Question

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.