\[\begin{array}{l}
m + \frac{1}{2}\left( {2x + 1} \right) + x = \left( {m + 1} \right)x - 3\\
\Leftrightarrow 2m + 2x + 1 + 2x = 2\left( {m + 1} \right)x - 6\\
\Leftrightarrow 4x + 2m + 1 - 2\left( {m + 1} \right)x + 6 = 0\\
\Leftrightarrow \left( {4 - 2m - 2} \right)x + 2m + 7 = 0\\
\Leftrightarrow \left( { - 2m + 2} \right)x + 2m + 7 = 0\,\,\left( * \right)\\
TH1: - 2m + 2 = 0 \Leftrightarrow m = 1\,thi\,\left( * \right)\,tro\,thanh\,9 = 0\left( {VN} \right)\\
TH2: - 2m + 2 \ne 0\,thi\,\left( * \right) \Leftrightarrow x = \frac{{2m + 7}}{{2m - 2}}\\
Vay\,neu\,m = 1\,thi\,pt\,VN\\
Neu\,m \ne 1\,thi\,pt\,co\,nghiem\,duy\,nhat\,x = \frac{{2m + 7}}{{2m - 2}}
\end{array}\]
