n, n + 2, n + 4 - three consecutive even integers
the twice the sum of the second and third: 2[(n + 2) + (n + 4)]
twelve less than six times the first: 6n - 12
The equation:
2[(n + 2) + (n + 4)] = 6n - 12
2(n + 2 + n + 4) = 6n - 12
2(2n + 6) = 6n - 12 use distributive property
(2)(2n) + (2)(6) = 6n - 12
4n + 12 = 6n - 12 subtract 12 from both sides
4n = 6n - 24 subtract 6n from both sides
-2n = -24 divide both sides by (-2)
n = 12
n + 2 = 12 + 2 = 14
n + 4 = 12 + 4 = 16
Answer: 12, 14, 16