# The sum of two consecutive odd integers is -116, what are the integers?

Mar 23, 2018

The two numbers are $- 59$ and $- 57$.

#### Explanation:

Say that one of our odd numbers is $x$. That would mean that the next odd number after $x$ would be $x + 2$ (because odd numbers are separated by an even number).

Since we know that their sum is $- 116$, we can set up an equation and solve for $x$:

$x + \left(x + 2\right) = - 116$

$x + x + 2 = - 116$

$2 x + 2 = - 116$

$2 x + 2 \textcolor{b l u e}{-} \textcolor{b l u e}{2} = - 116 \textcolor{b l u e}{-} \textcolor{b l u e}{2}$

$2 x \textcolor{red}{\cancel{\textcolor{b l a c k}{+} \textcolor{b l a c k}{2} \textcolor{b l u e}{-} \textcolor{b l u e}{2}}} = - 116 \textcolor{b l u e}{-} \textcolor{b l u e}{2}$

$2 x = - 116 \textcolor{b l u e}{-} \textcolor{b l u e}{2}$

$2 x = - 118$

$\frac{2 x}{2} = \frac{- 118}{2}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} = \frac{- 118}{2}$

$x = \frac{- 118}{2}$

$x = - 59$

This is our first odd number. We said that our other odd number would be $x + 2$, so, therefore, our numbers are $- 59$ and $- 59 + 2$, or $- 57$. Hope this helped!