Respuesta :
Answer: 258 different whole numbers
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Explanation:
502 < 385+a < 761
502 < a+385 < 761
502-385 < a+385-385 < 761-385 .... subtract 385 from all 3 sides
117 < a < 376
We can pick any number between 117 and 376, excluding both endpoints.
If 'a' is a whole number then we have 376-117-1 = 258 different choices and the solution set looks like this: {118, 119, ..., 374, 375}
The "-1" at the end is to exclude the upper endpoint. The lower endpoint is already excluded.
A smaller example: lets say you had the set {2,3,4,5,6,7}, we see that 7-2 = 5, but if we subtract 1 more from that we have 5-1 = 4 items that are between the endpoints 2 and 7.
So again there are 258 whole numbers between 117 and 376, such that we exclude the endpoints 117 and 376.
In other words, there are 258 different whole numbers we can pick for 'a' such that 502 < 385+a < 761 would be a true inequality.
If we let 'a' be any real number, then there are infinitely many choices we can pick.
