Question

The sum of two consecutive even integers is -134 . What are the two numbers?

Answer 1

2x + 2x+2 = -134
4x + 2 = -134
4x = -136 |: 4
x = -34

2x = 2 * (-34) = -68
2x + 2 = -68 + 2 = -66

This numbers are -66 and -68.

Answer 2

If we let x equal one of the numbers, and we let y equal the other number, we can define the equation as $x+y=-134$. Since we know, though, that the numbers are even and consecutive integers, we can say that $y=x+2$. We can then substitute our new value of y into the first equation which becomes $x+x+2=-134$. It can then be simplified as follows:
$x+x+2=-134 \\ 2x+2=-134 \\ 2x=-136 \\ x=-68$.
We have now solved for x, but we still need to know what y is, so we need the equation $y=x+2$ which we can evaluate and solve for y.
$y=x+2 \\ y=-68+2 \\ y=-66$
Now we have the two consecutive even integers whose sum is -134. They are -68 and -66.