Math Problem Statement
Solution
To solve part (a) of the question, we need to describe the union of the intervals shown in the two number line graphs using a compound inequality.
Analysis of the Graphs:
-
Top graph (green):
- The green line starts at (closed circle) and extends to 1 (open circle).
- This indicates that the inequality for the green line is:
-
Bottom graph (red):
- The red line starts at (closed circle) and extends to 3 (closed circle).
- This means the inequality for the red line is:
Union of the Two Graphs:
The union combines both intervals. Visually, the union covers the range from to 3.
- Starting from , the green line includes all values up to (but not including) 1, while the red line overlaps from and continues up to 3.
- The union will therefore cover all values from to 3, with:
- A closed boundary at ,
- An open boundary at 1,
- And a closed boundary at 3.
Compound Inequality:
The union of these intervals can be written as:
This is the compound inequality describing the union of the points in the graph.
Would you like any further details on this?
Here are 5 related questions to expand on this concept:
- What is the difference between union and intersection in terms of inequalities?
- How would you graph the intersection of these two sets?
- Can you explain how to solve compound inequalities involving "or" conditions?
- What are other methods to represent this union, such as interval notation?
- How do you solve inequalities when there are more complex combinations of "and" and "or" statements?
Tip: When dealing with compound inequalities, it helps to carefully consider both the boundaries (open and closed) and overlap between the intervals!
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Math Problem Analysis
Mathematical Concepts
Compound Inequalities
Graphing Inequalities
Union of Intervals
Formulas
Inequalities: a ≤ x < b
Theorems
Properties of inequalities
Union of intervals in set theory
Suitable Grade Level
Grades 8-10
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