# The greater of two consecutive even integers is six less than twice the smaller. What are the numbers?

Nov 29, 2016

8, 10

#### Explanation:

$n$ is the larger number and is even.

The even numbers are consecutive so the smaller number may be defined as $n - 2$.

$n = 2 \left(n - 2\right) - 6$
$n = 2 n - 4 - 6$
$n = 2 n - 10$

Subtract $n$ from both sides.
$0 = n - 10$
$10 = n$

$10$ is the larger number.

The smaller number must be $8$ because $8 \left(2\right) - 6 = 10$.