Answer
$(-\infty,2)$
Work Step by Step
We have:
$$\begin{aligned}
|x-1|=\begin{cases}
-x+1,x<1\\
x-1,x\geq 1.
\end{cases}
\end{aligned}$$ $$\begin{aligned}
|x-3|=\begin{cases}
-x+3,x<3\\
x-3,x\geq 3.
\end{cases}
\end{aligned}$$
The inequality can be written:
$$\begin{aligned}
-x+1&<-x+3,&&x<1\\
x-1&<-x+3,&&1\leq x<3\\
x-1&
