Answer:
Let's call the first of the three consecutive integers "x".
According to the problem, the third integer (which is the one after the first two) is equal to twice the first increased by five. We can express this algebraically as:
third integer = 2x + 5
Since the three integers are consecutive, the second integer must be one more than the first, and the third must be one more than the second. So, the second integer can be expressed as:
second integer = x + 1
And the third integer is:
third integer = (x + 1) + 1 = x + 2
Now we can set these two expressions for the third integer equal to each other, since they both represent the same value:
2x + 5 = x + 2
Simplifying and solving for x, we get:
x = -3
So the first of the three consecutive integers is -3. The second is one more than the first, which is -3 + 1 = -2. And the third is one more than the second, which is -2 + 1 = -1. Therefore, the three consecutive integers are -3, -2, and -1.