Chris W. answered • 09/27/17
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Near-daily Calculus Practitioner Since 2007
Since the problem statement told us that x is an integer, and we know that 8 is an integer as well, the only way to get a non-integer result is for 8 or x to be divided by the other; for instance, if x is 2, 8*x = 16 (an integer), x-8 = -6 (also an integer), but x/8 = 2/8 = 1/4 = 0.25 (not an integer!). If the number chosen alongside x had been something other than 8 (especially if it were not an integer) we would have to consider other cases! E.g., if we had been given 3/4,
(3/4)*x could be an integer, but it certainly isn't guaranteed.
