Find three consecutive even integers such that 4 times the first equals 16 times the sum of the third and the number 2

Consecutive even integers are numbers right in a row with a difference of two because they are even.

x= first integer
x+2= second integer
x+4= third integer

4 * x= 16((x + 4) + 2)
combine like terms in parentheses

4x= 16(x + 6)
multiply 16 by parentheses

4x= (16 * x) + (16 * 6)
4x= 16x + 96
Subtract 16x from both sides

-12x= 96
divide both sides by -12

x= -8 first consecutive even integer

x+2= -6 second cons. even integer
x+4= -4 third cons. even integer

ANSWER: The three consecutive even integers are -8, -6 and -4.

Hope this helps! :)