Answer:
-3, -1 and 1.
Step-by-step explanation:
If we define a number as [tex]x[/tex], the next odd number is [tex]x+2[/tex], and the next is [tex]x+4[/tex], so three consecutive odd integers are: [tex]x[/tex], [tex]x+2[/tex] and [tex]x+4[/tex].
the sum of these consecutive numbers is:
[tex]x+x+2+x+4\\=3x+6[/tex]
and six times that sum:
[tex]6(3x+6)[/tex] which is equal to: [tex]18x+36[/tex]
and the problem statement indicates that 6 times the sum of the three consecutive odd integers is equal to [tex]-18[/tex], so:
[tex]18x+36=-18[/tex]
clearing for x:
[tex]18x=-18-36[/tex]
[tex]18x=-54[/tex]
[tex]x=\frac{-54}{18} =-3[/tex]
so if [tex]x=-3[/tex], [tex]x+2=-1[/tex] and [tex]x+4=1[/tex]
the three integers are: -3, -1 and 1.
