please help me please

Question

six times the sum of tree consecutive odd integers is -18. what are the integers?

Answer 1

Hi Naomi!

So to start out this equation, let's identify what we know for sure.

1) there will be some multiplication of 6

2) We can denote "some number" or any number we don't know such as "integer" as "x"

3) there are 3 consecutive odd integers added together. In English, this means that each number + 2 is consecutive. ex: if we start with {5, 7, 9} as our consecutive integers, meaning they come right after one another, then we can write it as {5, (5)+2 =7, ( (5) +2)+2 = 7+2 = 9}, so on and so forth. Since we need to add them together, instead of commas we can replace those commas with addition signs later. In other words, we can't denote the integer as a number since we don't know it, so we have to denote it as a variable. or "x".

4) all of this is equal to -18

Let's translate this to math:

1) 6× (6 multiplied by)

2) (x) + (x+2) + (x+2)+2 (the sum of some consecutive odd integers)

3) =-18 (equals -18)

Now putting this all together, we will have:

6( x + (x+2) + (x+2)+2) = -18

or 6 times the sum of 3 consecutive odd integers that equal -18.

Now to solve this, we can combine like terms first, then multiply through using the distributive property, and finally solve the two step equation.

1) combine like terms (combine all x's with x's and numbers with numbers:

6( x+x+2+x+2+2)=-18

6( 3x + 6) = -18

2) distributive property

6*3x + 6*6 = -18

18x + 36 = -18

subtract 36 then divide by 18.

18x = -54

x = -3

So now that we solved for x and checked that it is indeed odd, we will know that the consecutive integers will also be odd once we plug it back into the equation.

first odd integer: -3

second odd integer after -3: -3 +2 = -1

Third odd integer after -1: -1 +2 = 1

So in the end after checking if this is true, the list of integers is: {-3 , -1 , 1}

If you have any questions or would like me to clarify don't hesitate to ask. I wish you good luck with your math class!

Answer 2

6(3x) = -18

x = -18/18 = -1

x-2 = -3

x = -1

x+2 = 1

the numbers are

-3, -1 and +1

6 times the sum of 3 odd integers is 6(x-2+x+x+2) = 6(3x) = 18x

18x =-18

x =-1, x-2 = -3, x+2 = +1