SOLUTION: What are the three consecutive even integers so that the value three times the second integer is equal to six more than the sum of the first and third integers?

Question 800548: What are the three consecutive even integers so that the value three times the second integer is equal to six more than the sum of the first and third integers?
Answer by thepianist25(8) (Show Source): You can put this solution on YOUR website!
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
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