Final answer:
The three consecutive integers can be represented as x, x+1, and x+2. The sum of these integers is equal to 2 times the smallest integer. By solving the equation, we find that the smallest integer is -3.
Step-by-step explanation:
In this problem, we are looking for three consecutive integers whose sum is twice the smallest integer. Let's assume the smallest integer is x. The next two consecutive integers would be x+1 and x+2.
The sum of these three consecutive integers would be x + (x+1) + (x+2).
According to the problem, this sum is twice the smallest integer, so we can write the equation: x + (x+1) + (x+2) = 2x.
Simplifying the equation, we get: 3x + 3 = 2x.
Subtracting 2x from both sides, we get: x + 3 = 0.
Subtracting 3 from both sides, we get: x = -3.
Therefore, the smallest integer is -3.