Answer:
The numbers that meet these conditions are -3, -2 and -1.
This means that the wording of the question is somewhat ambiguous:
The lowest of the three numbers is -3.
The smallest however is -1.
You may need clarification on which of those is being asked for.
Explanation:
Let's call those numbers a, b and c, with a the smallest and c the largest. We're told two key things here:
1) The sum of the smaller two integers is two more than seven times the largest integer. In other words a + b = 7c + 2
2) We're looking for three consecutive integers, which means that we can define them with a single variable. If the smallest one is a, then the others are a + 1 and a + 2.
We can take those and put them together, giving us the equation:
a + (a + 1) = 7(a + 2) + 2
Which we can then solve for a:
a + (a + 1) = 7(a + 2) + 2
2a + 1 = 7a + 14 + 2
2a - 7a = 14 + 2 - 1
-5a = 15
a = -3
Since a is -3 and also the smallest, we can then say that the numbers are -3, -2 and -1.