Question

If 9x is an odd integer, represent the next odd integer as the algebraic expression in x.

Answer 1

Any odd integer can be expressed as 2n+1, for some integer n.

The next odd integer, after 2n+1, is 2n+1+2=2n+3



thus 9x=2n+1, means that 9x-1=2n,   so n=(9x-1)/2

the next odd number after 2n+1 is 2n+3= 2* (9x-1)/2+3=9x-1+3=9x+2


Remark : this result could also have been found directly.


Answer: 9x+2