\(\left|x+1\right|-2x=3\)
\(\Rightarrow\left|x+1\right|=3+2x\)
\(\Rightarrow\left[{}\begin{matrix}x+1=3+2x\\x+1=-2x-3\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x-2x=3-1\\-2x-x=1+3\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-2\\x=-\dfrac{4}{3}\end{matrix}\right.\)