The sum of three consecutive integers is 33. Find the smallest integer:

To find the smallest integer, let's represent the three consecutive integers algebraically. If the smallest integer is 'x', then the next two consecutive integers would be 'x + 1' and 'x + 2'. The problem states that their sum is 33. So, we set up the equation: x + (x + 1) + (x + 2) = 33. Combining like terms, we get 3x + 3 = 33. Subtracting 3 from both sides gives 3x = 30. Dividing by 3, we find x = 10. Therefore, the smallest integer is 10. The other options would not satisfy the condition of summing to 33 with their consecutive counterparts.