$a)|x-1|+|3-x|=2$
$|x-1+3-x|=2$
$|x-4-x|=2$
$|2x-4|=2$
`=>`\(\left[ \begin{array}{l}2x-4=2\\2x-4=-2\end{array} \right.\)`=>` \(\left[ \begin{array}{l}x=3\\x=1\end{array} \right.\)
$b)|x-2|+|x-3|=1$
$|x-2+x-3|=1$
$|2x-5|=1$
`=>`\(\left[ \begin{array}{l}2x-5=1\\2x-5=-1\end{array} \right.\)`=>` \(\left[ \begin{array}{l}x=3\\x=2\end{array} \right.\)
