Solve the inequality and graph the solution.

Question

2p≥16
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 \(2p \geq 16\), we first divide both sides by 2:

\[ p \geq 8 \]

This means that \(p\) can be any value greater than or equal to 8.

Steps to Graph the Solution:

1. Find the endpoint: The endpoint of the solution is 8.

2. Choose endpoint type: Since the inequality is greater than or equal to (≥), we will use a closed dot at \(p = 8\) to indicate that 8 is included in the solution set.

3. Determine direction: The solution \(p \geq 8\) implies that we need to shade to the right of 8, representing all values greater than 8.

4. Select an endpoint to change: Suppose we want to change the closed dot at 8 to an open dot (but this would change the solution). Instead, we’ll keep it closed as per the original condition.

5. Select the middle of the segment to delete: For this inequality, there's no segment to delete since it's a ray starting from 8 and extending to positive infinity.

Graph of the Solution

• You will have a closed dot at 8.
• A shaded line (or ray) extending to the right from 8, indicating all numbers greater than 8.

Here's a simple representation of the graph:

<----●========================>
        8

In this graph:

• The ◯ (closed dot) at 8 indicates that 8 is included in the solution.
• The shaded line indicates all values greater than 8.