By the binomial theorem,
[tex]\left(\dfrac x3+\dfrac9{x^2}\right)^7=\displaystyle\sum_{n=0}^7\binom7n\left(\frac x3\right)^{7-n}\left(\frac9{x^2}\right)^7=\sum_{n=0}^7\binom7n\left(\frac3x\right)^{3n-7}[/tex]
We get the [tex]x[/tex] term when 3n - 7 = -1, or n = 2, which has coefficient
[tex]\dbinom723^{3\cdot2-7}=\boxed{7}[/tex]
