Math Problem Statement
Solution
The interval represented on the number line is from to , where is included (denoted by the filled circle) and is not included (denoted by the open circle). Let's analyze each expression to see if it represents this interval:
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A. : This is correct because it means is between and , including but excluding , which matches the graph.
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B. : This is incorrect because it excludes (the open inequality) and includes , which doesn't match the number line.
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C. : This is incorrect because this notation excludes both and , whereas the graph includes .
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D. : This is correct because this notation means is between and , including and excluding , which matches the graph.
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E. : This is incorrect because it implies that is strictly greater than , excluding , which doesn't match the number line.
So, the correct answers are A and D.
Would you like further clarification on any of these? Here are some related questions for more practice:
- How would you write the interval if both and were included?
- What does the notation represent?
- How would you describe the set of numbers ?
- What is the difference between open and closed intervals in terms of notation?
- How would the inequality look if neither nor were included?
Tip: When dealing with intervals, pay close attention to the type of bracket or inequality. Square brackets mean the value is included, while parentheses mean the value is excluded.
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Math Problem Analysis
Mathematical Concepts
Intervals
Inequalities
Set Notation
Formulas
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Theorems
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Suitable Grade Level
Grades 7-9