\(\Rightarrow\left|1-x\right|=\sqrt{2}-\dfrac{1}{9}\\ \Rightarrow\left[{}\begin{matrix}1-x=\sqrt{2}-\dfrac{1}{9}\\x-1=\sqrt{2}-\dfrac{1}{9}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1-\sqrt{2}+\dfrac{1}{9}=\dfrac{10}{9}-\sqrt{2}\\x=\sqrt{2}-\dfrac{1}{9}+1=\dfrac{8}{9}+\sqrt{2}\end{matrix}\right.\)