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

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...

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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

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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

Approved by eNotes Editorial Team