To solve the inequality \( g - 7 \geq 1 \), follow these steps:
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Isolate \( g \): \[ g - 7 \geq 1 \] Add \( 7 \) to both sides: \[ g \geq 1 + 7 \] \[ g \geq 8 \]
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Determine critical points: The critical point where the inequality holds is \( g = 8 \).
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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 \( 8 \).
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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.