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In the given problem, you are asked to graph the solution set of the linear inequality \( x > 4 \) or \( y \geq 2 \).

Here is a breakdown of how to proceed with the graphing:

### 1. **Inequality \( x > 4 \)**:
   - This inequality represents a vertical line at \( x = 4 \). Since it's a strict inequality, the boundary line will be dashed.
   - We choose two points on the line, such as \( (4, 0) \) and \( (4, 1) \), but the line itself will not be part of the solution since \( x > 4 \). We will shade the region to the right of the line (where \( x > 4 \)).

### 2. **Inequality \( y \geq 2 \)**:
   - This inequality represents a horizontal line at \( y = 2 \). Since it's a non-strict inequality (with \( \geq \)), the boundary line will be solid.
   - Choose two points, such as \( (0, 2) \) and \( (1, 2) \), and shade the region above the line where \( y \geq 2 \).

### 3. **Shading the region**:
   - Since this is an "OR" inequality, you will shade the regions that satisfy either inequality. This means you will shade the region to the right of \( x = 4 \) and the region above \( y = 2 \).
   - You can ignore any areas where neither inequality holds.

### Input for the Graph:
- For the boundary line of \( x = 4 \):
   - Choose "Dashed" for the line.
   - Points: \( (4, 0) \), \( (4, 1) \).
   - Shade to the right (Region B).
  
- For the boundary line of \( y = 2 \):
   - Choose "Solid" for the line.
   - Points: \( (0, 2) \), \( (1, 2) \).
   - Shade above (Region A).

Would you like more details on this process, or any further clarification?

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Here are 5 related questions to expand your understanding:
1. How do you graph inequalities involving both \( x \) and \( y \)?
2. How would the solution change if the inequality were \( x \geq 4 \) or \( y > 2 \)?
3. What does the union of two inequality regions (OR) represent geometrically?
4. How do you shade regions for "AND" inequalities, and how is it different from "OR"?
5. How would you represent inequalities that include variables on both sides, such as \( 2x + y > 4 \)?

**Tip**: Always check if the inequality includes an "or equal to" condition (like \( \geq \) or \( \leq \)), as this determines if the boundary line is solid or dashed.

Graph the solution set of the first linear inequality: x > 4 or y ≥ 2.

Learn how to graph the solution set of the linear inequality x > 4 or y ≥ 2 with a detailed step-by-step solution. This problem covers key algebraic concepts, including graphing linear inequalities. Suitable for students in Grades 9-12.

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