Question

The sum of three consecutive even integers is 126. Let x represent the least consecutive integer.

Answer 1

Just as an example, three consecutive integers might be 4,5,6.

If x is the least of these (4 in our example), then the other two integers would be x+1, and x+2.

Then the sum of our three integers is x + (x+1) + (x+2). 

Addition is commutative so we can switch any two terms, and it is also associative so we can regroup any terms. This lets is rearrange things with all the "x" together and all the numbers together like this:

(x+x+x) + (1+2) OR 3x + 3

According to the problem, the sum is 126, so 3x+3 = 126.
3x = 123
x = 41 (which is the smallest consecutive integer)

Check our answer: 41 + 42 + 43 = 126.