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Let's call the smallest of the consecutive odd integers x. Then the other ones are x+2 and x+4 respectively, and your equation becomes 4*(x+x+2)+7 = 7*(x+4) which is equivalent to 8x+15=7x+28 or x=13, so the consecutive integers you're looking for are 13, 15 and 17.

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Q: Three consecutive odd integers such that four times the sum of the first and second is 7 less than 7 times the third?
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