The sum of three consecutive even integers is 126. let x represent the least consecutive integra. what is the greatest consecutive integer?

First, we need to see how to get from one even integer to another. Well, what do you do to get from 2 to 4? 4 to 6? You add 2. If x is even, then the next even number must be x+2, and then the next x+4, and x+6, and so on. Since we're only going 3, we have:
x + (x+2) + (x+4) = 126. Now we can just solve the equation!

x + x + 2 + x + 4 = 126
3x + 6 = 126.
3x = 120.
x=40. But is that your answer? Nope! Don't forget, the problem says that x is the smallest number out of the 3. Which means 40 + 2 is the middle number, and 40 + 4 = 44 is the greatest.

Your answer is 44.

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