If we represent the least integer with the variable x, then the middle integer would be x + 1, and the greatest would be x + 2.
Then the sum of the least and greatest would be written as: x + x + 2
Also 12 more than the middle integer would be written as: x + 1 + 12
Since these two expressions are equal to each other, we can write: x + x + 2 = x + 1 + 12
Now combine like terms and use inverse operations to solve for x (the least integer):
x + x + 2 = x + 1 + 12
2x + 2 = x + 13
2x - x + 2 = x + 13 - x
x + 2 = 13
x + 2 - 2 = 13 - 2
x = 11
The least integer will be 11.
The middle integer will be 12.
The greatest integer will be 13.
To verify: the sum of the least and the greatest is 11 + 13 = 24
This is indeed 12 more than the middle integer of 12.
