Answer: Let's call the smallest of the three consecutive integers "x". Then the next two integers will be "x+1" and "x+2".
We know that the sum of the three integers is twice the largest integer plus 11. We can use this information to set up the following equation:
x + (x+1) + (x+2) = 2(x+2) + 11
Simplifying, we get:
3x + 3 = 2x + 5 + 11
So we can get:
x = 3
Therefore, the three consecutive integers are 3, 4 and 5.
Explanation: