If half of the smaller of two consecutive even integers is 2 more than the larger, what are the integers?

Oct 3, 2015

The integers are $\left(- 8\right)$ and $\left(- 6\right)$

Explanation:

Let the two consecutive even integers be
$\textcolor{w h i t e}{\text{XXX}} 2 n$ and $2 n + 2$

We are told:
$\textcolor{w h i t e}{\text{XXX}} \frac{1}{2} \cdot \left(2 n\right) = \left(2 n + 2\right) + 2$

Simplifying
$\textcolor{w h i t e}{\text{XXX}} n = 2 n + 4$

$\textcolor{w h i t e}{\text{XXX}} - n = 4$

$\textcolor{w h i t e}{\text{XXX}} n = - 4$

The numbers are
$\textcolor{w h i t e}{\text{XXX}} 2 n = - 8$
and
$\textcolor{w h i t e}{\text{XXX}} 2 n + 2 = - 6$