Two even integers are represented by 2n and 2n+2. Explain how you can find the value of those integers if their sum is 14. Name the integers.

4n+2 = 14 ?

4 n = 12

n=3

2n = 6
2n+2 = 8

Thank you

To find the value of two even integers represented by 2n and 2n+2, we will proceed as follows:

Step 1: Set up the equation representing the sum of the two integers.
Let's assume the first even integer is represented by 2n, and the second even integer is represented by 2n+2. The sum of these two integers is 14, so we can write the equation as: (2n) + (2n+2) = 14.

Step 2: Simplify the equation.
To simplify, we add the terms in the equation: 2n + 2n + 2 = 14.
Combine like terms: 4n + 2 = 14.

Step 3: Isolate the variable.
To isolate the variable, subtract 2 from both sides of the equation: 4n + 2 - 2 = 14 - 2.
Simplify: 4n = 12.

Step 4: Solve for n.
Divide both sides of the equation by 4 to solve for n: 4n/4 = 12/4.
Simplify: n = 3.

Step 5: Substitute n back into the original expressions to find the integers.
Substitute n = 3 into the expressions for the even integers:
The first even integer is represented by 2n = 2(3) = 6.
The second even integer is represented by 2n+2 = 2(3) + 2 = 8.

Therefore, the two even integers are 6 and 8, respectively.

To find the value of the two even integers, we can set up an equation based on the given information.

Let's assume the first even integer is represented by 2n, where n is a whole number. The second even integer would then be represented by 2n+2.

Since the sum of these two integers is 14, we can write the equation:

2n + (2n+2) = 14

Now, let's solve this equation step-by-step to find the value of n and the corresponding integers:

2n + 2n + 2 = 14 (Combine like terms)

4n + 2 = 14 (Simplify)

4n = 14 - 2 (Subtract 2 from both sides)

4n = 12 (Simplify)

n = 12 / 4 (Divide both sides by 4)

n = 3 (n is 3)

So, the first even integer can be calculated by substituting n = 3 into 2n:

2(3) = 6

Therefore, the first even integer is 6.

Now, substituting n = 3 into 2n+2, we can find the second even integer:

2(3) + 2 = 6 + 2 = 8

Therefore, the second even integer is 8.

To summarize, the two even integers are 6 and 8, respectively.