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find the positive difference between to consecutive even integers such that 14 times the first is equal to 12 times the second

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Huh? The difference between any two consecutive even integers is 2!

14(2k) = 12(2k+2)
28k = 24k+24
4k = 24
k = 6

the numbers are 12 and 14, so the difference is 2

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