Find three consecutive odd integers such that six times the second decreased by twice the third is equal to twelve less than the sum of the first and second

Question

Im so confused help me plz

Answer 1

Let n be the first integer, Then the next odd integer has to be n + 2 and the third odd integer n + 4

So six times the second integer is 6 x ( n + 2) decreased by twice the third is"

6 x ( n + 2) - 2 x ( n + 4 ) This is equal to twelve less than the sum of the first and second, namely

n + ( n + 2 ) - 12 Putting it all together we have the equation

6 x ( n + 2 ) - 2 x ( n + 4 ) = n + ( n + 2 ) -12 Multiplying out

6 x n 12 - 2 x n - 8 = 2 x n - 10

4 x n + 4 = 2 x n - 10

or 2 x n = .14 and n = -7 So the three consecutive odd integers are: -7, -5, -3

You can check this to see that it works

Answer 2

Hi Tianna,

First you need to understand how to designate the three integers or numbers.

Of course, in algebra, x can be any number.

But you need it to be odd.

The only way to guarantee that any integer comes out odd is to double it and then subtract 1.

So you double the x to get 2x... then you subtract 1... 2x-1.

In these problems, whenever you need an odd integer, you can think about it as I have written above, or you can just memorize that an odd integer is 2x-1.

So we need three odd integers that are consecutive (in a row).

So, we let the first one be

2x - 1

Now to get the next odd integer after that one, we would have to count up 2 numbers. So that would be the 2x - 1 plus 2. This comes out to 2x + 1.

Then to get the third integer, we would take the second one which is 2x + 1 and add 2 to that. We get

2x + 3.

So we can designate three consecutive odd integers as...

2x - 1 (integer #1)

2x + 1 (integer #2) and

2x + 3 (integer #3)

If that makes sense to you, keep going. If not, go back and think through that again.

Now we need "six times the second"

That would be six multiplied by (2x + 1), the second integer, which is 6(2x + 1). Distribute to get...

12x + 6.

We will decrease that by "twice the third."

What is twice the third? Two multiplied by the third integer 2x + 3. That is 2(2x + 3). Distribute to get...

4x + 6 ("twice the third").

So six times the second decreased by twice the third

is....

12x + 6 minus 4x + 6. Or

12x + 6 - (4x + 6)

The problem says that expression "is".... "Is" means = . They made it easy on you by saying "is equal to" instead of just "is." Remembering that "is" means = is sometimes a big help to students.

Anyway...

It equals "twelve less than the sum of the first and second."

First we need the sum of the first and the second.

That would be the sum of (2x - 1) and (2x + 1). Sum means "add," so the sum is...

(2x - 1) + (2x + 1) which is

2x - 1 + 2x + 1, which is

4x.

We need "twelve less than this sum," which is

4x - 12.

So...

12x + 6 - (4x + 6) is equal to 4x - 12.

Or

12x + 6 - (4x + 6) = 4x - 12

Be careful with the minus sign in front of the parenthesis.

Next step is

12x + 6 - 4x - 6 = 4x - 12

Now just do the simple algebra to solve for x.

Then plug your answer for x back into the expressions for the three integers...

2x - 1

2x + 1 and

2x + 3

and "voila"... you have your three consecutive integers.

Note that for this problem, they are all three negative integers!