+)Xét $x< 1$$\Rightarrow\begin{cases}x-1< 0\Rightarrow\left|x-1\right|=-\left(x-1\right)=-x+1\\x-3< 0\Rightarrow\left|x-3\right|=-\left(x-3\right)=-x+3\end{cases}$

$pt\Leftrightarrow\left(-x+1\right)+\left(-x+3\right)=2$

$\Leftrightarrow4-2x=2\Leftrightarrow2x=2\Leftrightarrow x=1$ (loại, do x<1)

+)Xét $1\le x&lt; 3$$\Rightarrow\begin{cases}x\ge1\Rightarrow x-1\ge0\Rightarrow\left|x-1\right|=x-1\\x&lt; 3\Rightarrow x-3&lt; 0\Rightarrow\left|x-3\right|=-\left(x-3\right)=-x+3\end{cases}$

$pt\Leftrightarrow\left(x-1\right)+\left(-x+3\right)=2$

$\Leftrightarrow2=2\Rightarrow x\in R$

+)Xét $x\ge3$$\Rightarrow\begin{cases}x-1\ge0\Rightarrow\left|x-1\right|=x-1\\x-3\ge0\Rightarrow\left|x-3\right|=x-3\end{cases}$

$pt\Leftrightarrow\left(x-1\right)+\left(x-3\right)=2$

$\Leftrightarrow2x-4=2\Leftrightarrow2x=6\Leftrightarrow x=3$ (thỏa mãn)