Math Problem Statement
Graph the solution set of the first linear inequality: x > 4 or y ≥ 2.
Solution
In the given problem, you are asked to graph the solution set of the linear inequality or .
Here is a breakdown of how to proceed with the graphing:
1. Inequality :
- This inequality represents a vertical line at . Since it's a strict inequality, the boundary line will be dashed.
- We choose two points on the line, such as and , but the line itself will not be part of the solution since . We will shade the region to the right of the line (where ).
2. Inequality :
- This inequality represents a horizontal line at . Since it's a non-strict inequality (with ), the boundary line will be solid.
- Choose two points, such as and , and shade the region above the line where .
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 and the region above .
- You can ignore any areas where neither inequality holds.
Input for the Graph:
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For the boundary line of :
- Choose "Dashed" for the line.
- Points: , .
- Shade to the right (Region B).
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For the boundary line of :
- Choose "Solid" for the line.
- Points: , .
- Shade above (Region A).
Would you like more details on this process, or any further clarification?
Here are 5 related questions to expand your understanding:
- How do you graph inequalities involving both and ?
- How would the solution change if the inequality were or ?
- What does the union of two inequality regions (OR) represent geometrically?
- How do you shade regions for "AND" inequalities, and how is it different from "OR"?
- How would you represent inequalities that include variables on both sides, such as ?
Tip: Always check if the inequality includes an "or equal to" condition (like or ), as this determines if the boundary line is solid or dashed.
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Math Problem Analysis
Mathematical Concepts
Linear Inequalities
Graphing Inequalities
Formulas
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Theorems
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Suitable Grade Level
Grades 9-12