\(|x+1|+|x+2|=3x \,\,(ĐK : 3x\geq0) \\ \Leftrightarrow \left[ \begin{array}{l}(x+1)+(x+2)=3x\\-(x+1)-(x+2)=3x\end{array} \right. \\ \Leftrightarrow \left[ \begin{array}{l}x+1+x+2=3x\\-x-1-x-2=3x \end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x+x-3x=-1-2\\-x-x-3x=1+2\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}-x=-3\\-5x=3\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x=3\,\,(TM)\\x=\dfrac{-5}{3}\,\,\text{(loại do}\,\,3x=-5<0)\end{array} \right. \\ \text{Vậy}\,\,x=3\)