Of three consecutive even integers, the sum of the smallest two integers is equal to 6 less than the largest. Find the integers

Answer 1

Three consecutive even integers have the form 2k, 2k+2, 2k+4 for some integer (to be found) k. The sum of the smallest two is equal to 2k+(2k+2)=4k+2. If I understand correctly what you mean by saying 6 less than the largest we must have that 4k+2=2k+4-6 which gives us the equation 4k+2=2k-2 or equivalently 2k=-4 which implies that k=-2. Hence, the consecutive even integers that you are trying to find are the numbers -4, -2, 0.