How do you find four consecutive even integers such that -4 times the sum of the first and fourth is 6 greater than the opposite of the sum of the second and third?

Jun 18, 2018

Is 'the opposite of the sum' subtraction?

Explanation:

Any number is $n$, to ensure it is even we use $2 n$

The four consecutive numbers will be

$2 n , 2 n + 2 , 2 n + 4 , 2 n + 6$

$- 4 \left(2 n + 2 n + 6\right) > \left(2 n + 4 - 2 n - 2\right)$

$- 4 \left(4 n + 6\right) > 2$

$- 16 n - 24 > 2$

add $16 n$

$- 24 > 16 n + 2$#

subtract 2

$- 26 > 16 n$

divide by 16

$- \frac{26}{16} > n$

$- \frac{13}{8} > n$