=>|4x|=-2x+11
\(\Leftrightarrow\left\{{}\begin{matrix}\left(4x\right)^2-\left(-2x+11\right)^2=0\\x< =\dfrac{11}{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left(4x+2x-11\right)\left(4x-2x+11\right)=0\\x< =\dfrac{11}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(6x-11\right)\left(2x+11\right)=0\\x< =\dfrac{11}{2}\end{matrix}\right.\Leftrightarrow x\in\left\{\dfrac{11}{6};-\dfrac{11}{2}\right\}\)
\(\left|4x\right|=-2x+11\left(x\text{≤ }\dfrac{11}{2}\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}-4x=-2x+11\\-4x=2x-11\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=-11\\6x=11\end{matrix}\right.\left[{}\begin{matrix}x=\dfrac{11}{2}\\x=\dfrac{11}{6}\end{matrix}\right.\)