Circuit Analysis in Non-Closed Systems

Question

So I'm fairly confident in my ability to do circuit analysis on closed circuits, that is, circuits where all loops, sources, and elements are given. However I still find myself getting stuck on circuits where only a particular section of the system is given.

For example: In a problem I'm trying to solve, it is asked to use Thevenin's theorem to simplify this circuit:

I'm honestly quite lost, I understand that the voltages given at the terminals are relative to ground, but I have no idea how to translate those into an equivalent source. My first instinct would be to start by reducing the outside parallel resistances, which would reduce the circuit down to a T-shape with equivalent resistances of 5 ohms on each side. From there I'm stuck. Would I add the voltages as sources in series with the resistor?

Any intuition on best practice when considering systems like this would be appreciated. Thanks!

Edit: So I think I understand, flipping around some signs, would the following be an appropriate representation?

Edit2: Diagram with common ground

Answer 1

This is an intuitive way I can solve this in my head in << 1 minute. You may use KCL,KCL.

^{simulate this circuit – Schematic created using CircuitLab}

^{simulate this circuit}

^{simulate this circuit}