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 + (n + 2) + (n + 4) + (n + 6) = -28
Solving for n gives:
n + n + 2 + n + 4 + n + 6 = -28
n + n + n + n + 2 + 4 + 6 = -28
4n + 12 = -28
4n + 12 - color(red)(12) = -28 - color(red)(12
4n + 0 = -40
4n = -40
(4n)/color(red)(4) = -40/color(red)(4)
(color(red)(cancel(color(black)(4)))n)/cancel(color(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
