\(\left|x+1\right|=\left|2x+3\right|\\ \Leftrightarrow\left(x+1\right)^2=\left(2x+3\right)^2\\ \Leftrightarrow x^2+2x+1=4x^2+12x+9\\ \Leftrightarrow x^2+2x+1-4x-12x-9=0\\ \Leftrightarrow-3x^2-10x-8=0\\ \Leftrightarrow-3x^2-6x-4x-8=0\\ \Leftrightarrow-3x\left(x+2\right)-4\left(x+2\right)=0\\ -\left(x+2\right)\left(3x+4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x+2=0\\3x+4=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-2\\x=-\dfrac{4}{3}\end{matrix}\right.\)
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