Math Problem Statement
a. Choose the correct interval notation for the inequality notation x > −3
[-3, ∞)
(-3, ∞)
(-∞ , -3)
(-∞ , 3) None of these
b. Choose the correct interval notation for the inequality notation −3 < x ≤ 3 or 7 ≤ x
(-3, 3] ⋃ [7, ∞)
(-3, 3) ⋃ (7, ∞)
[-3, 3) ⋃ [7, ∞)
[-3, 3] ⋃ (7, ∞) None of these
c. Choose the correct interval notation for the inequality notation x ≤ −3 or 7 ≤ x
(-∞ , -3] ⋃ (7, ∞)
(-∞ , -3) ⋃ (7, ∞)
(-∞ , -3] ⋃ [7, ∞)
(-∞ , 3) ⋃ (7, ∞) None of these
Solution
Let's analyze and solve each part:
a. Choose the correct interval notation for the inequality notation :
The inequality means that starts just above and goes to infinity. In interval notation, we express this as:
- is not included, so we use a parenthesis.
- Infinity is always accompanied by a parenthesis.
Answer for (a):
b. Choose the correct interval notation for the inequality notation or :
This represents two intervals:
-
: is between and , but is not included while is included.
- Interval:
-
: starts at 7 (included) and goes to infinity.
- Interval:
The union () of these intervals is:
Answer for (b):
c. Choose the correct interval notation for the inequality notation or :
This represents two intervals:
-
: starts from negative infinity up to (including ).
- Interval:
-
: starts at 7 (included) and goes to infinity.
- Interval:
The union () of these intervals is:
Answer for (c):
Summary of correct answers:
- a:
- b:
- c:
Would you like further details or explanations on any of these solutions?
5 Related Questions:
- How do you express strict inequalities in interval notation?
- What is the difference between open and closed intervals in inequalities?
- How would you express in interval notation?
- How do you represent a union of intervals in set notation?
- What does an intersection of two intervals mean in terms of inequalities?
Tip:
Always use parentheses for strict inequalities ( or ) and brackets for inclusive inequalities ( or ).
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Math Problem Analysis
Mathematical Concepts
Inequalities
Interval Notation
Set Union
Formulas
No specific formula, but involves interpreting inequalities and intervals
Theorems
No specific theorem, but involves set theory and interval notation rules
Suitable Grade Level
Grades 9-12