The sum of 4 consecutive negative odd numbers is -32. What are the numbers?

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Assume that the first number is x

Then the sum is:

x+ (x+2) + (x+4) + (x+6) =-32

4x + 12 = -32

4x = -32 -12 = -44

==> x= -11

Then the numbers are:

-11, -9, -7 , and -5 ( All odd, negative, and consecutive)

To check:

-11 + -9 + -7 + -5 = -32

Consecutive integers can be expressed as x, x+1, x+2 etc, however we do not want consecutive integers, we want consecutive odd integers that are also negative. Consecutive odd integers are 2 apart from eachother so we can adjust the list for consecutive integers to either odd or even by changing the +1 to +2, like this, x, x+2, x+4, x+6 etc. those 4 will give us the 4 we need, now the question is, do we need to do anything in particular to address the issue of the integers being negative?

I don't think so, we don't know if x is positive or negative it just represents the number and numbers we need to add to -32 so if it is negative it will show up that way when we solve for x.

so x+x+2+x+4+x+6=-32 is the equation we are going to work with, we need to combine like terms which gives us

4x+12=-32

subtract 12 from both sides of the equal sign

4x+12-12=-32-12

combine like terms

4x=-44 (-32+(-12))

divide both sides by 4

(4x/4)=(-44/4)

x=-11 so our 4 consecutive negative odd integers should be

-11,-9,-7,-5 which we check by adding them and they do indeed add to -32

4 odd numbers should sum up -32 . So we can just assume x is an odd number and the 4 consecutive negative odd numbers greater than x are x+2, x+4, x+6. So their sum = x+x+2+x+4+x+6 = 4x+12 must be equal -32 by the given condtion.

Threfore 4x = -32-12 = -44

x= -44/4 = -11

Therefore the 4 consecutive odd numbers are :

-11, -9, -7 and -5

Let the first number be -n. Then the four consecutive negative odd numbers will be:

-n, (-n -2), (-n -4) and (-n -6)

And the sum of these 4 numbers will be:

-n + (-n -2) + (-n -4) + (-n -6)

= -n - n -2 - n - 4 - n - 6

= -4n - 12

As the sum pf the numbers is given as -32

-4n - 12 = -32

-4n = -32 + 12 = -20

Therefore:

n = (-20)/(-4) = 5

Therefore the four consecutive negative odd numbers are:

-5, -7, -9 and -11

Let's consider 4 consecutive negative odd numbers:

-t-2, -t-4, -t-6, -t-8

Their sum is -32:

-t-2-t-4-t-6-t-8 = -32

-4t = -32+20

-4t = -12

We'll multiply by -1 both sides:

4t = 12

We'll divide by 4:

t = 12/4

t = 3

The numbers are:

-t-2 = -3-2 = -5

-t-4 = -3-4 = -7

-t-6 = -3-6 = -9

-t-8 = -3-8 = -11

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