Newbie's electric circuit simplification question

[beborche]

Homework Statement

Simplify the circuit as much as possible to prepare it for node analysis.

Homework Equations

KCL (sum of all currents through a node equal zero)
Ohm's law V=RI

The Attempt at a Solution

I'd like to use node analysis. But first I have simplified the circuit and landed at this new circuit:

I have no key answer to look at and I feel rather insecure at electronics. Are my simplifications correct? I.e. are those two circuits equivalent?

Thanks.

 

[KataKoniK]

To prepare the circuit for node analysis, we can combine the two resistors in parallel into one equivalent resistor using the formula 1/R_eq = 1/R1 + 1/R2. This will give us a simplified circuit with only one resistor and one voltage source. We can then apply Ohm's law and KCL to solve for the unknown values in the circuit.