a) Ta có: \(\left|x-4\right|=3x+2\)
\(\Leftrightarrow\left[{}\begin{matrix}x-4=3x+2\left(x\ge4\right)\\4-x=3x+2\left(x< 4\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-3x=2+4\\-x-3x=2-4\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}-2x=6\\-4x=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-3\left(loại\right)\\x=\dfrac{1}{2}\left(nhận\right)\end{matrix}\right.\)
b) Ta có: \(\left|-4x\right|=x+3\)
\(\Leftrightarrow\left[{}\begin{matrix}-4x=x+3\left(x\le0\right)\\4x=x+3\left(x>0\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}-4x-x=3\\4x-x=3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}-5x=3\\3x=3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{3}{5}\left(nhận\right)\\x=1\left(nhận\right)\end{matrix}\right.\)
