Solve the inequality and graph the solution.

Question

g–7≥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 \( g - 7 \geq 1 \), follow these steps:

1. Isolate \( g \): \[ g - 7 \geq 1 \] Add \( 7 \) to both sides: \[ g \geq 1 + 7 \] \[ g \geq 8 \]

2. Determine critical points: The critical point where the inequality holds is \( g = 8 \).

3. Graph the solution:

   • Since \( g \geq 8 \), you will plot the point \( 8 \) on a number line.
   • Use a closed circle at \( 8 \) because the inequality is inclusive (i.e., \( g \) can equal \( 8 \)).
   • Shade the line to the right of \( 8 \) to indicate all values greater than \( 8 \).

4. Summary of graph:

   • You plot \( 8 \) with a closed circle.
   • The area to the right of \( 8 \) (all numbers greater than \( 8 \)) is shaded to indicate it’s part of the solution set.

Here's how the graph would look:

<---|------|------|------|------|------|------|------|------|------|--->
   6      7      8      9     10     11     12     13     14     15
                •====================>

• Here, \( • \) represents a closed circle at \( 8 \), and the arrow indicates that the solution set extends indefinitely to the right.