# The sum of two consecutive integers is −13. What are the numbers?

##### 1 Answer
May 5, 2016

$- 7 - 6 = - 13$

#### Explanation:

$\textcolor{b l u e}{\text{There are other ways of solving this but I have opted to demonstrate a}}$
$\textcolor{b l u e}{\text{method that can be used for other condition. For example:}}$$\textcolor{b l u e}{\text{The sum of 3 consecutive odd numbers and the next even number is 71}}$

$\textcolor{b r o w n}{\text{ 15, 17, 19 and 20} \to \left(n\right) + \left(n + 2\right) + \left(n + 4\right) + \left(n + 5\right) = 71}$
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Let the first number be $n$
Let the second number be $n + 1$

Then $\text{ } n + n + 1 = - 13$

$2 n + 1 = - 13$

Subtract 1 from both sides

$2 n = - 13 - 1 = - 14$

Divide both sides by 2

$\frac{2}{2} \times n = - \frac{14}{2}$

But $\frac{2}{2} = 1$

$n = - 7$

So the second number is $\text{ } - 7 + 1 = - 6$