In effort to solve for Vx, I would like to transform the Delta network (the 3 3 ohm resistors) to a Y network. My question is, where would Vx be read ?
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It will be between the same two points (you should have marked the points). But it would become more difficult for you to analyze the circuit.
However, you can approach in another way - Apply source transformation to 1ohm resister & 3Ix current source which will give you 3 mesh. Apply KVL to three mesh and solve further to find Vx.
PS: I'm assuming you're familiar with source transformation and Mesh analysis techniques.