Math Problem Statement
Solution
The inequality given is . You are asked to express this using interval notation and illustrate it on the real number line.
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Interval Notation: The inequality means that can take any value between 7 and 9, inclusive of both endpoints. The interval notation for this is: The square brackets indicate that the endpoints 7 and 9 are included in the interval.
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Correct Graph: On the real number line, this interval is represented by a solid line between 7 and 9 with closed circles at both ends, indicating that the endpoints are included.
Based on the image, Graph D correctly represents the inequality with a solid line between 7 and 9 and closed circles at both 7 and 9.
Would you like more details on how to solve similar inequalities, or do you have any further questions?
Here are five related questions you could explore:
- How do you solve compound inequalities?
- What is the difference between strict inequalities and non-strict inequalities in interval notation?
- How do you represent inequalities with infinity in interval notation?
- How do you solve inequalities involving absolute values?
- What are the steps to graph inequalities with more complex expressions?
Tip: When using interval notation, always check if the inequality includes or excludes the endpoints—this determines whether to use parentheses or brackets.
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Math Problem Analysis
Mathematical Concepts
Algebra
Inequalities
Interval Notation
Formulas
Interval notation for inequalities
Real number line representation
Theorems
Inequality Representation Theorem
Suitable Grade Level
Grades 6-8