Ta có: -2x-11 chia hết cho 3x+2
\(\Rightarrow\)-3(-2x-11)\(⋮\)3x+2
hay 6x+33\(⋮\)3x+2
\(\Rightarrow6x+4+29⋮3x+2\)
\(\Rightarrow29⋮\left(3x+2\right)\)
\(\Rightarrow3x+2\inƯ\left(29\right)\)
\(\Leftrightarrow3x+2\in\left\{1;-1;29;-29\right\}\)
\(\Leftrightarrow3x\in\left\{-1;-3;27;-31\right\}\)
\(\Rightarrow x\in\left\{\frac{-1}{3};-1;9;\frac{-31}{3}\right\}\)
mà \(x\in Z\)
nên \(x\in\left\{-1;9\right\}\)
Vậy: \(x\in\left\{-1;9\right\}\)