Are these valid transformations, Please guide
Yes those transformations are allowed since they are in series.



And here's why mathematically, we can see to the left that it's 21 V across the rightmost branch. 

This gives you the following KVL equation:

\$21 = 3I+60+10I\$

And that is the exact same thing as 

\$
21 = 60+13I\\
21 = 13I+60
\$