a: |x-1|=2x+1
\(\Leftrightarrow\left\{{}\begin{matrix}x>=-\dfrac{1}{2}\\\left(2x+1\right)^2=\left(x-1\right)^2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>=-\dfrac{1}{2}\\\left(2x+1+x-1\right)\left(2x+1-x+1\right)=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x>=-\dfrac{1}{2}\\3x\left(x+2\right)=0\end{matrix}\right.\Leftrightarrow x=0\)
b: \(\left|x-3\right|=2x-9\)
\(\Leftrightarrow\left\{{}\begin{matrix}x>=\dfrac{9}{2}\\\left(2x-9-x+3\right)\left(2x-9+x-3\right)=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x>=\dfrac{9}{2}\\\left(x-6\right)\left(3x-12\right)=0\end{matrix}\right.\Leftrightarrow x=6\)
c: =>|x-2|=2x+3
\(\Leftrightarrow\left\{{}\begin{matrix}x>=-\dfrac{3}{2}\\\left(2x+3-x+2\right)\left(2x+3+x-2\right)=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x>=-\dfrac{3}{2}\\\left(x+5\right)\left(3x+1\right)=0\end{matrix}\right.\Leftrightarrow x=-\dfrac{1}{3}\)
d: =>x+1=x-3 hoặc x+1=3-x
=>2x=2
hay x=1
