Question

Six times the sum of three consecutive odd integers is -18. What are the integers?

Answer 1

1, -1, -3

Explanation:

6(x+x+2+x+4)=-18

6(3x+6)=-18

18x+36=-18

18x=-54

x=-3

so x=-3, x+2=-1, and x+4=1

Answer 2

-3, -1 and 1.

Explanation:

If we define a number as
`x`, the next odd number is
`x+2`, and the next is
`x+4`, so three consecutive odd integers are:
`x`,
`x+2` and
`x+4`.

the sum of these consecutive numbers is:

`x+x+2+x+4\\=3x+6`

and six times that sum:

`6(3x+6)` which is equal to:
`18x+36`

and the problem statement indicates that 6 times the sum of the three consecutive odd integers is equal to
`-18`, so:

`18x+36=-18`

clearing for x:

`18x=-18-36`

`18x=-54`

`x=(-54)/(18) =-3`

so if
`x=-3`,
`x+2=-1` and
`x+4=1`

the three integers are: -3, -1 and 1.