\(3\left|x-1\right|-5=7\)
\(\Rightarrow3\left|x-1\right|=7+5\)
\(\Rightarrow3\left|x-1\right|=12\)
\(\Rightarrow\left|x-1\right|=12:3\)
\(\Rightarrow\left|x-1\right|=4\)
\(\Rightarrow\left[{}\begin{matrix}x-1=4\\x-1=-4\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=5\\x=-3\end{matrix}\right.\)
Vậy, \(x\in\left\{-3;5\right\}\)