Question

The smaller of two consecutive even integers is two more than half of the greater. find the two integers.

Answer 1

Greetings and Happy Holidays!

Let x represent the smaller, even integer.
Let (x+2) represent the larger, even integer.

We can create an algebraic equation to solve for the numbers:

`x=((x+2))/(2)+2`

Simplify:

`x=(1)/(2)x+1+2`


`x=(1)/(2)x+3`

Add
`(-1)/(2)x` to both sides:

`(x)+((-1)/(2)x)=((1)/(2)x+3)+((-1)/(2)x)`


`((1)/(2)x)=3`

Divide both sides by
`(1)/(2)x`

`((1)/(2)x)/( (1)/(2))=(3)/((1)/(2))`


`x=(3)/(1)(2)`


`x=(6)/(1)`

The Answer Is:

`\boxed{x=6}`
and

`x+2=6`

`\boxed{x=8}`

The two consecutive even integers are 6 and 8.

I hope this helped!
-Benjamin