Final answer:
The consecutive odd integers whose sum is -15 are -7, -5, and -3. This is found by setting up an equation with x representing the first integer and solving for the sum of x, x+2, and x+4.
Step-by-step explanation:
To find consecutive odd integers whose sum is -15, we can use algebra to set up an equation. Let's say the first odd integer is x, then the next consecutive odd integer would be x+2 (since odd integers are two units apart), and so on depending on how many integers we are looking for.
If we are looking for two consecutive odd integers whose sum is -15, our equation would be:
x + (x+2) = -15
Solving for x gives us:
- 2x + 2 = -15
- 2x = -15 - 2
- 2x = -17
- x = -17/2
- x = -8.5
However, -8.5 is not an integer. Since the question specifies that the integers are odd, this result is not useful. Thus we must assume we are dealing with more than two integers. In practice, three integers often produce solvable equations for this sort of problem.
So, let us try three consecutive odd integers, x, x + 2, and x + 4. The sum then is:
x + (x+2) + (x+4) = -15
Solving for x:
- 3x + 6 = -15
- 3x = -21
- x = -21 / 3
- x = -7
Therefore, the three consecutive odd integers are -7, -5, and -3 since their sum equals -15:
-7 + (-5) + (-3) = -15