Three consecutive even integers have the property that when the sum of the first integer and twice the second is found, the result is eight more than the third. What is the largest integer?

The three consecutive integers are 4,6,8.

Explanation:

There's a gap of 2 units between adjacent neighboring numbers. Consecutive even integers are numbers like 2,4,6,... or 10,12,14,... They are even numbers and they follow one right after another.

The sum of the first and twice the second is 8 more than the third, so,

first + 2*(second) = (third) + 8

We'll plug in the expressions defined above and solve for x

x + 2*(x+2) = (x+4) + 8

x + 2x+4 = x+4+8

3x+4 = x+12

3x-x = 12-4

2x = 8

x = 8/2

x = 4 is the first number

x+2 = 4+2 = 6 is the second number

x+4 = 4+4 = 8 is the third number and the largest