+)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 \(1\le x< 3\)\(\Rightarrow\begin{cases}x\ge1\Rightarrow x-1\ge0\Rightarrow\left|x-1\right|=x-1\\x< 3\Rightarrow x-3< 0\Rightarrow\left|x-3\right|=-\left(x-3\right)=-x+3\end{cases}\)

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

\(\Leftrightarrow2=2\Rightarrow x\in R\)

+)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)