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The numbers represented by variables a and c, on the number line, are integers. If c > b > a, under which of the following conditions could the expression b > 5 be true?

A. When a = 5
B. When a = 10
C. When a = 7 and c = 3
D. When a = -6 and c = -1

User Achref
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1 Answer

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Final answer:

The expression b > 5 could be true when a = 5, a = 10, or when a = -6 and c = -1. It could not be true when a = 7 and c = 3 because c must be greater than b, but in this case, it is not.

Step-by-step explanation:

The student asked under which conditions the expression b > 5 could be true given that c > b > a and both a and c are integers on the number line. To solve this, we examine each given condition.

  • A. When a = 5, since b must be greater than a, b could be 6 or any integer greater, making b > 5 true.
  • B. When a = 10, b has to be greater than 10, which makes b definitely greater than 5.
  • C. When a = 7 and c = 3, this condition cannot be true because a must be less than b and c should be greater than b, but here c is less than a.
  • D. When a = -6 and c = -1, since b must be between a and c, b could be -5, -4, -3, -2, or any integer greater than -6 and less than -1, which means b could be greater than 5.

Therefore, in conditions A, B, and D, the expression b > 5 could be true. The only scenario where b > 5 is not guaranteed is condition C.

User Djokovic
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