\(\sqrt{\left(1-2x\right)^2}=9\)
<=> \(\sqrt{\left(1-2x\right)^2}=3^2\)
<=> \(\left|1-2x\right|=\left|3\right|\)
<=> \(\left|1-2x\right|=3\)
<=> \(\left[{}\begin{matrix}1-2x=3\\1-2x=-3\end{matrix}\right.\)
<=> \(\left[{}\begin{matrix}x=-1\\x=2\end{matrix}\right.\)
\(\sqrt{\left(1-2x\right)^2}=9\)
\(\Rightarrow\left|1-2x\right|=9\)
\(\Rightarrow\left[{}\begin{matrix}1-2x=9\\1-2x=-9\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-4\\x=5\end{matrix}\right.\)