[tex]\begin{gathered} \frac{2x+3}{9}>\frac{x}{3}+1 \\ \frac{2x+3}{9}>\frac{x+3}{3} \\ 3(2x+3)>9(x+3) \\ 6x+9>9x+27 \\ 6x-9x>27-9 \\ -3x>18 \\ \frac{\cancel{-3}x}{\cancel{-3}}>\frac{18}{\cancel{-3}},\text{ dividing by negative on both sides, flips the inequality} \\ x<-6 \end{gathered}[/tex]
