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

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