# What three consecutive integers have a sum of -33?

May 8, 2018

$- 12 , - 11 , - 10$

#### Explanation:

You could solve this by guessing and checking, but such a strategy might be difficult for numbers larger or smaller than $- 33$. As such, we will use an algebraic approach to solve this.

We are told that the sum of three consecutive integers is $- 33$. Let's call the lowest of these three integers $x$. Since the numbers are consecutive, it must be the case that the next smallest integer is $x + 1$ and the greatest integer is $x + 2$.

So we can rewrite the problem as the algebraic statement $x + \left(x + 1\right) + \left(x + 2\right) = - 33$. The rest is algebra.

$x + \left(x + 1\right) + \left(x + 2\right) = - 33$
$x + x + 1 + x + 2 = - 33$
$3 x + 3 = - 33$
$3 x = - 36$
$x = - 12$

Our lowest integers is $- 12$. It follows that our next two integers are $- 11$ and $- 10$. We confirm that $- 12 - 11 - 10 = - 23 - 10 = - 33$.