Ideal Voltage/Current Source Circuit Analysis
It's probably conceptually easier to keep the wire there, and treat the total current as the sum of two currents in the wire.

If you look at the right hand loop, you know that the 4mA source is forcing 4mA through the wire. You don't have to work out what its voltage is, or anything around the 5k resistor. Just the fact that it's a current source means that 4mA will flow.

That means you can solve the left hand loop by itself. What Vx, given that you are given the value of 1k for the resistor, will force 4mA through the wire, in a direction to cancel out the current source's 4mA, to give a total of zero?