https://file.aiquickdraw.com/mathbot/file/1730398681613aa0pk6j9.jpg

To identify the graph that represents the inequality \( x \geq 2 \), let's analyze each option.

1. **Inequality**: \( x \geq 2 \) implies that the shaded region should include all points where \( x \) is greater than or equal to \( 2 \).
2. **Line**: The boundary line should be at \( x = 2 \). Since it is \( \geq \) (greater than or equal to), the line itself should be solid, indicating that points on the line \( x = 2 \) are included in the solution.
3. **Shaded Region**: The shading should be on the right side of this line, where \( x \) values are greater than 2.

### Analysis of Each Graph:

- **Top left**: Shows a solid vertical line at \( x = 2 \) with shading to the right, representing \( x \geq 2 \). This graph is correct.
- **Top right**: Shaded to the left of the line \( x = 2 \), which represents \( x \leq 2 \).
- **Bottom left**: Shaded to the right of the line \( x = 2 \), but the line is dashed, indicating \( x > 2 \) (not \( x \geq 2 \)).
- **Bottom right**: Shaded to the left of a dashed line at \( x = 2 \), which represents \( x < 2 \).

### Conclusion:
The correct answer is the **top left graph**, as it correctly represents \( x \geq 2 \) with a solid line at \( x = 2 \) and shading to the right.

Would you like more details on solving inequalities or graph interpretation?

### Related Questions:
1. How do you graph inequalities on a coordinate plane?
2. What is the difference between a solid line and a dashed line in inequality graphs?
3. How do you determine the direction of shading in inequality graphs?
4. What are the steps to solve a linear inequality and graph it?
5. How can inequalities be used to define regions in real-world applications?

**Tip**: For inequalities with "greater than or equal to" or "less than or equal to," use a solid line; for strict inequalities, use a dashed line.

Which graph represents the inequality x ≥ 2?

Learn how to graph the inequality x ≥ 2 on a coordinate plane. This problem covers key algebraic concepts, including identifying the correct shaded region for an inequality and understanding solid and dashed boundary lines. Suitable for students in Grades 6-8.

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