Question
Solve the inequality and graph the solution.
p/1 ≥-2
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.
p/1 ≥-2
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
GPT-4o mini
To solve the inequality \( \frac{p}{1} \ge -2 \), we can simplify the expression:
\[
p \ge -2
\]
This inequality indicates that \( p \) is greater than or equal to \(-2\).
### Step 1: Identify the endpoints
The endpoint for this inequality is \( -2 \).
### Step 2: Determine if the endpoint is closed or open
Since the inequality includes \( \ge \), we represent \(-2\) as a closed endpoint.
### Step 3: Graph the solution
To graph this solution:
- Plot the point \( -2 \) on a number line and make it a closed dot (indicating that \(-2\) is included in the solution set).
- Shade the region to the right of \(-2\) to indicate that all values greater than \(-2\) are included in the solution.
### Step 4: Modify the graph as per instructions
1. Select an endpoint to change it from closed to open. If you choose to make \(-2\) open, you would represent \(-2\) with an open dot (indicating it is not included in the solution).
2. Since the inequality is already set to emphasize the greater values (indicating a ray extending to the right), you do not need to delete any segments or rays.
### Final Result
The graph now looks like this:
- **Endpoint**: Open dot at \(-2\) (if changed from closed).
- **Region Shaded**: All values greater than \(-2\) to the right.
### Conclusion
The final solution is the inequality \( p > -2 \), and it is represented with an open dot at \(-2\) and a shaded line to the right.
\[
p \ge -2
\]
This inequality indicates that \( p \) is greater than or equal to \(-2\).
### Step 1: Identify the endpoints
The endpoint for this inequality is \( -2 \).
### Step 2: Determine if the endpoint is closed or open
Since the inequality includes \( \ge \), we represent \(-2\) as a closed endpoint.
### Step 3: Graph the solution
To graph this solution:
- Plot the point \( -2 \) on a number line and make it a closed dot (indicating that \(-2\) is included in the solution set).
- Shade the region to the right of \(-2\) to indicate that all values greater than \(-2\) are included in the solution.
### Step 4: Modify the graph as per instructions
1. Select an endpoint to change it from closed to open. If you choose to make \(-2\) open, you would represent \(-2\) with an open dot (indicating it is not included in the solution).
2. Since the inequality is already set to emphasize the greater values (indicating a ray extending to the right), you do not need to delete any segments or rays.
### Final Result
The graph now looks like this:
- **Endpoint**: Open dot at \(-2\) (if changed from closed).
- **Region Shaded**: All values greater than \(-2\) to the right.
### Conclusion
The final solution is the inequality \( p > -2 \), and it is represented with an open dot at \(-2\) and a shaded line to the right.