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.