Question

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

Answer 1

The integers are `(-8)` and `(-6)`

Explanation:

Let the two consecutive even integers be
`color(white)("XXX")2n` and `2n+2`

We are told:
`color(white)("XXX")1/2*(2n)=(2n+2)+2`

Simplifying
`color(white)("XXX")n=2n+4`

`color(white)("XXX")-n=4`

`color(white)("XXX")n=-4`

The numbers are
`color(white)("XXX")2n = -8`
and
`color(white)("XXX")2n+2=-6`