What three consecutive integers have a sum of -33?

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What three consecutive integers have a sum of -33?

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Answer 1 · 2018-05-08T19:30:33

$-12, -11, -10$

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 $x + (x+1) + (x+2) = -33$ . The rest is algebra.

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

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

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What three consecutive integers have a sum of -33?

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