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If a and b are the coordinates of two points on the number line, then which of the following is equivalent to the statement that the absolute distance from a to b is greater than the absolute distance from -2 to 6 ?
  • a)
    |a| > -2 and |b| > 6
  • b)
    |a - b| > -8
  • c)
    |a + 2| > |b - 6|
  • d)
    |a - b| > 8
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If a and b are the coordinates of two points on the number line, then ...
Explanation:

Understanding the question:
The absolute distance from a to b is represented by |a - b|, and the absolute distance from -2 to 6 is represented by |-2 - 6| = |-8| = 8.

Given Statement:
We need to determine which of the following statements is equivalent to |a - b| > 8.

Analyzing the options:
a) |a| > -2 and |b| > 6 - This statement does not represent the absolute distance between a and b.
b) |a - b| > -8 - This statement does not accurately represent the comparison of absolute distances between a and b and -2 to 6.
c) |a + 2| > |b - 6| - This statement does not represent the absolute distance between a and b.
d) |a - b| > 8 - This statement accurately represents the comparison of absolute distances between a and b and -2 to 6.

Conclusion:
Option D, |a - b| > 8, is equivalent to the statement that the absolute distance from a to b is greater than the absolute distance from -2 to 6.
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Community Answer
If a and b are the coordinates of two points on the number line, then ...
The absolute distance from a to b is |a - b| and the absolute distance from -2 to 6 is |-2 - 6| = 8. Therefore, |a - b| > 8.
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If a and b are the coordinates of two points on the number line, then which of the following is equivalent to the statement that the absolute distance from a to b is greater than the absolute distance from -2 to 6 ?a)|a| > -2 and |b| > 6b)|a - b| > -8c)|a + 2| > |b - 6|d)|a - b| > 8Correct answer is option 'D'. Can you explain this answer?
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