\(\left|x-1\right|+\left|2x-2\right|=9\\ \Rightarrow\left|x-1\right|+2\left|x-1\right|=9\\ \Rightarrow3\left|x-1\right|=9\\ \Rightarrow\left|x-1\right|=3\\ \Rightarrow\left[{}\begin{matrix}x-1=3\\x-1=-3\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=4\\x=-2\end{matrix}\right.\)