Julie has three children whose ages are consecutive odd integers. if x represents the youngest childs age, which expression represents the sum of her childrens ages

X = first child
x +2 = 2nd child
x+ 4 = 3rd child

It doesn't matter if the ages are odd or even - there is two years between each child in age.

The sum would be
x + x + 2 + x + 4 or  3x + 6.
Lets try it with a sample age.  Let's say the youngest is 5 middle is 7 and oldest is 9
The sum of their ages is 21 (5 + 7 + 9)

Using our answer of 3x + 6 where x is the age of the youngest child, we get
3(5) +6 which is also 21.

This could also be solved by having x represent the middle age child
x-2 is the youngest (2 years less than the middle)
x = the middle
x+2 is the oldest (2 years older than the middle)

The sum of these would be x-2 + x + x +2  or simply 3x (the 2's cancel out)
Since the middle child is 7   3x would mean 3 (7)=21

You could also set this up using x for the oldest child
x= oldest
x-2= middle
x-4= youngest   (The sum of this is 3x - 6)

3 (9) -6 is also 21.