INTEGERS PLEASE HELP

Question

There are three consecutive odd integers where the product of the first and second integers is  less than  times the third.

What three consecutive odd integers fit this description?

Answer 1

The question is ambiguous, but maybe it means

first times 2nd is less than that product times the third consecutive number

FS < FST

x(x+2) < x(x+2)(x+4)

divide by x

x+2 < x^2 +6x + 8 (if x>0),

but reverse the inequality sign if x<0

0< x^2 +5x +6

0< (x+3)(x+2) makes both (x+3) and (x+2)>0 and x>0

0>(x+3)(x+2) for x<0 means (x+3) and (x+2) are opposite signs

(x+3)>0 and (x+2)<0, x>-3 and x<-2, so -3<x<-2 which is impossible if x is an integer

or

(x+3)<0 and (x+2)>0, x<-3 and x>-2 which is impossible

x>0, x+2> 2, x+4>4

consecutive odd integers are 1,3, and 5

or 3,5, and 7

or 5, 7, and 9

or 1+n, 3+n and 5+n where n= any positive integer

such as

567, 569 and 571