Question:
Given that \( X \) is the set of all integers \( n \) that satisfy the inequality \( 2 \leq |n| \leq 5 \), compare the following quantities:
\[
\text{The absolute value of the greatest integer in } X \quad \text{and} \quad \text{The absolute value of the least integer in } X
\]
Given that \( X \) is the set of all integers \( n \) that satisfy the inequality \( 2 \leq |n| \leq 5 \), compare the following quantities:
\[
\text{The absolute value of the greatest integer in } X \quad \text{and} \quad \text{The absolute value of the least integer in } X
\]
Show Hint
When comparing the absolute values of integers, remember that the absolute value is always non-negative, and both positive and negative numbers of the same magnitude have the same absolute value.
Updated On: Oct 7, 2025
- Quantity A is greater
- Quantity B is greater
- The two quantities are equal
- The relationship cannot be determined from the information given.
Show Solution
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The Correct Option is D
Solution and Explanation
Step 1: Understand the set \( X \).
The set \( X \) consists of integers \( n \) such that \( 2 \leq |n| \leq 5 \), so the possible values of \( n \) are \( -5, -4, -3, 3, 4, 5 \).
Step 2: Compare the quantities.
The greatest integer in \( X \) is 5, and the least integer in \( X \) is -5. The absolute value of both of these integers is 5. Therefore, the two quantities are equal.
Step 3: Conclusion.
Thus, the correct answer is that the two quantities are equal.
Final Answer: \[ \boxed{\text{The correct answer is (3) The two quantities are equal.}} \]
The set \( X \) consists of integers \( n \) such that \( 2 \leq |n| \leq 5 \), so the possible values of \( n \) are \( -5, -4, -3, 3, 4, 5 \).
Step 2: Compare the quantities.
The greatest integer in \( X \) is 5, and the least integer in \( X \) is -5. The absolute value of both of these integers is 5. Therefore, the two quantities are equal.
Step 3: Conclusion.
Thus, the correct answer is that the two quantities are equal.
Final Answer: \[ \boxed{\text{The correct answer is (3) The two quantities are equal.}} \]
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