# How do you find three consecutive integers whose sum is -93?

May 27, 2016

$\left\{- 32 , - 31 , - 30\right\}$

#### Explanation:

Let $n$ be the least of the three consecutive integers. Then the integers are $n , n + 1$, and $n + 2$, and we have that

$n + \left(n + 1\right) + \left(n + 2\right) = - 93$

$\implies 3 n + 3 = - 93$

$\implies 3 n = - 96$

$\implies n = - 32$

Substituting that into $\left\{n , n + 1 , n + 2\right\}$, we get the solution set $\left\{- 32 , - 31 , - 30\right\}$