Question 800548
To solve this word problem, you will need to set up an equation.  When working with problems using consecutive (in a row) integers, it is helpful to visualize an example in your mind or on paper to know what is being discussed.  In this case, 3 consecutive even integers are being used. So you know that it will look something like 2, 4, 6, or 10, 12, 14, etc.

So with the information being given, I should first write down the important stuff:

First integer: x (this is what I am starting with)
Second integer: x + 2 (if x was 2, then to get to the next even number, I would have to use x + 2)
Third integer: x + 4 (if x was 2, then to get to the third number, I would have to use x + 4)

Now I look at the other information in the problem:

The value three times the second integer: 

3(x + 2), since the second integer is x + 2

Is equal to:

=

Six more than the sum of the first and third integers:

(x + x + 4) + 6, since the first and third integers respectively are x and x + 4

Now, I can set up my equation:

3(x + 2) = (x + x + 4) + 6
3x + 6 = (x + x + 4) + 6
3x + 6 = 2x + 4 + 6
3x + 6 = 2x + 10
3x - 2x + 6 = 2x - 2x + 10 (subtraction axiom)
x + 6 = 10
x + 6 - 6 = 10 - 6 (subtraction axiom)
x = 4

So, my integers are:

First: x = 4
Second: x + 2 = 6
Third: x + 4 = 8