Math Problem Statement
Graph the inequality x ≤ 3.
Solution
To graph the inequality , we need to follow these steps:
Step-by-Step Instructions:
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Draw the Boundary Line:
- The inequality involves the vertical line at .
- Since the inequality includes (less than or equal to), the boundary line should be solid because points on the line satisfy the inequality.
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Plot Points on the Boundary:
- Identify points on the line where . Examples of such points are , , and .
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Shade the Region:
- The inequality means all values of that are less than or equal to 3.
- Shade the region to the left of the vertical line at because that represents the values where is less than or equal to 3.
Summary:
- Solid vertical line at .
- Shade the region to the left of this line.
Would you like more details on this process or have any further questions?
Here are 5 related questions to expand this understanding:
- What happens if the inequality was instead of ?
- How would you graph the inequality ?
- How can you determine whether to use a solid or dashed line for inequalities?
- What changes if the inequality involves both and , like ?
- How do you handle graphing inequalities with horizontal lines, like ?
Tip: Always remember that a solid line means the boundary points are included (e.g., or ), while a dashed line means they are not (e.g., or ).
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Math Problem Analysis
Mathematical Concepts
Inequalities
Coordinate Plane Graphing
Formulas
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Theorems
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Suitable Grade Level
Grades 6-8