Answer:
\(2x+9⋮3x+1\)
\(\Rightarrow3\left(2x+9\right)⋮3x+1\)
\(\Rightarrow6x+27⋮3x+1\)
\(\Rightarrow2\left(3x+1\right)+25⋮3x+1\)
\(\Rightarrow25⋮3x+1\)
\(\Rightarrow3x+1\inƯ\left(25\right)=\left\{\pm1;\pm5;\pm25\right\}\)
\(\Rightarrow3x\in\left\{-2;0;-6;4;-26;24\right\}\)
\(\Rightarrow x\in\left\{0;-2;8\right\}\)