Question

Please help 100 points

The sum of three consecutive even integers is 36. Let x represent the first integer, x + 2 represent the
second integer, and x + 4 represent the third integer. What is the first integer?

Answer 1

The sum of three consecutive even integers is 36.

Let x represent the first integer

Because they are consecutive even integers,

x + 2 represent the second integer and x + 4 represent the third integer

so x + x + 2 + x + 4 = 36

3x + 6 = 36

3x = 30

x = 10

Answer 2

To find the answer to this question, we need to set up an equation and solve. Since we know that the sum of 3 numbers is 36, we know that we have something that will be equal to 36. We also know what our integers are (as they are given to us). Our integers are x, x + 2 and x + 4. Since the question says the sum of these integers is equal to 36, we know that sum means plus and equal means has the same value, that means that:

x + (x + 2) + (x + 4) = 36

Now we need to combine like terms. Like terms are terms that share a variable or don't have variables at all. After some rearranging, we get:

(x + x + x) + (2 + 4) = 36

Simplifying gives us:

3x + 6 = 36

Now, we need to get the x on one side and the numbers on the other. This can be achieved by subtracting 6 from each side of the equation. This will get rid of the six on the side with the x (by subtracting six from both sides of the equation, we don't change it's value).

3x + 6 - 6 = 36 - 6

3x = 30

Now, we want to divide both sides by the coefficient of x (the number in front of x).

3/3x = 30/3

x = 10

That means that the first integer is 10.