Đáp án: $x=\dfrac{2}{5}$
Giải thích các bước giải:
$\left | x-1 \right |+\left | x-2 \right |=3x+1\\\Leftrightarrow \left | x-1 \right |+\left | x-2 \right |-3x=1\\\Leftrightarrow \left[ \begin{array}{l}x-1+x-2-3x=1,x-1\geq 0,x-2\geq 0\\-(x-1)+x-2-3x=1,x-1<0,x-2\geq 0\\x-1-(x-2)-3x=1,x-1\geq 0,x-2<0\\-(x-1)-(x-2)-3x=1,x-1<0,x-2<0\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x=-4,x-1\geq 0,x-2\geq 0\\x=-\frac{2}{3},x-1<0,x-2\geq 0\\x=0,x-1\geq 0,x-2<0\\x=\dfrac{2}{5},x-1<0,x-2<0\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x\in \varnothing \\x\in \varnothing \\x\in \varnothing \\x=\dfrac{2}{5}\end{array} \right.$
