To solve the inequality \(7 \leq f + 9\), we first isolate \(f\).
- Subtract 9 from both sides: \[ 7 - 9 \leq f \] \[ -2 \leq f \] This can also be written as: \[ f \geq -2 \]
The solution to the inequality \(f \geq -2\) means that \(f\) takes all values greater than or equal to \(-2\).
Graphing the Solution:
- To graph \(f \geq -2\), we plot the point \(-2\) on a number line.
- Since the inequality is "greater than or equal to," we use a closed dot at \(-2\) to indicate that \(-2\) is included in the solution set.
- We then shade the line to the right of \(-2\) to indicate that all values greater than \(-2\) are included.
Performing the specified actions:
- Plot the endpoints: The endpoint here is \(-2\) with a closed dot.
- Select an endpoint to change it from closed to open: If we were to select \(-2\) and change from closed to open, we would plot an open circle at \(-2\) instead.
- Select the middle of the segment, ray, or line to delete it: Since this is a ray extending to the right (positive direction), the "middle of the line" doesn't apply clearly in this case. Instead, we could note that an arbitrary point could be omitted from shading, but it doesn't particularly alter the representation of \(f \geq -2\).
Final Representation:
- Initial solution: \(f \geq -2\) with the closed circle at \(-2\).
- If we change \(-2\) to an open circle:
(open circle) to mark that it's not included, and shading to the right of \(-2\).
Note: Since this is a text-based representation, you can visualize it by drawing a horizontal line and marking the points as instructed.