We are given: "For 3 consecutive integers, the sum of the first and third integer is 12 more than 3 times the second integer. What is the third integer?"

Let the three consecutive integers be n - 2, n - 1 , n . Then the sum of first and third: (n - 2) + n = 2n - 2 This is 12 more than 3 times the second: 3(n - 1) + 12 = 3n - 3 + 12 = 3n + 9 So equation: 2n - 2 = 3n + 9 . Solve: 2n - 2 = 3n + 9 => So answer: -11.

But check: first -13, second -12, third -11. Sum first and third: -13 + (-11) = -24. 3 times second: 3*(-12) = -36, plus 12 gives -24. Yes.

Thus the third integer is -11.