# Question 10e8c

Jan 27, 2017

See the entire solution process below:

#### Explanation:

First, let's define the four consecutive even integers.

We can call the first even integer: $n$

The other 3 consecutive even integers will be by adding $2$ to the previous integer (consecutive even integers are always 2 numbers apart).

So, the integers are:

$n$, $n + 2$, $n + 2 + 2 = n + 4$ and $n + 4 + 2 = n + 6$

The sum of these four numbers equals $- 28$ or:

$n + \left(n + 2\right) + \left(n + 4\right) + \left(n + 6\right) = - 28$

Solving for $n$ gives:

$n + n + 2 + n + 4 + n + 6 = - 28$

$n + n + n + n + 2 + 4 + 6 = - 28$

$4 n + 12 = - 28$

4n + 12 - color(red)(12) = -28 - color(red)(12#

$4 n + 0 = - 40$

$4 n = - 40$

$\frac{4 n}{\textcolor{red}{4}} = - \frac{40}{\textcolor{red}{4}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} n}{\cancel{\textcolor{red}{4}}} = - 10$

$n = - 10$

$n + 2 = - 10 + 2 = - 8$

$n + 4 = - 10 + 4 = - 6$

$n + 6 = - 10 + 6 = - 4$

The four consecutive even integers adding to -28 are:

$- 10$, $- 8$, $- 6$ and $- 4$