Find three consecutive even integers with a sum of -12

Question

I cant figure this out I need help

Answer 1

Consecutive even integers follow the following pattern: 2x, 2x + 2, 2x + 4, ... , 2x + n

If you want to find the sum you need to add the first three expressions in the pattern and set it equal to -12 so that you end up with an equation like this:

(2x) + (2x + 2) + (2x + 4) = -12 or 2x + 2x + 2 + 2x + 4 = -12

Then you combine like terms:

6x + 6 = -12

And, solve for the first integer which we can call x₁.

To find the second integer (x₂), plug in x₁ to the second expression in the sequence, 2x +2.

2(x₁) + 2 = x₂

To find the third integer (x₃), plug in x₂ to the third expression in the sequence, 2x + 4.

2(x₂) + 4 = x₃

Check your work by adding the three integers and setting it equal to -12:

x₁ + x₂ + x₃ = -12

So, for example, if I want to find three consecutive even integers with a sum -20, then...

6(x₁) + 6 = -20

6(x₁) = -26

x₁ = -4.333...

2(-4.333...) + 2 = x₂

-8.667 + 2 = x₂

-6.667 = x₂

2(-6.667) + 4 = x₃

-13.333... + 4 = x₃

-9.333... = x₃

x₁ + x₂ + x₃ = -20

* I had to round so it should will not add up to -20 exactly instead it adds up to -20.332

*(-4.333) + (-6.667) + (-9.333) ≅ -20

Hope this helps!

Answer 2

Hi.

Thank you for your question. In order to solve this problem, you first need to understand the terminology in the question.

What are integers?

Integers are whole numbers. They van be positive or negative.

What does consecutive mean?

This means the numbers are "in a row," like 1, 2, 3 or -5, -4, -3. However, this questions asks for consecutive even integers. Those would be even numbers in a row like 2, 4, 6 or -8, -6, -4.

What does sum mean?

It's the total when you add them up.

Now that we understand the question, a simple guess and check method could work for this problem.

We want these three numbers to add up to -12, so they must be negative.

Let's try adding -2, -4, and -6.

They equal -12!

We did it on the first try :)

Great work!