Thevenin equivalent with dependet sources

What is the motivation behind your second equation?

 

I see. Well, it doesn't look like a valid equation to me.

Here's a trick that often helps with these types of circuits. If you consider a general Thevenin source it's a voltage supply Vth with a series resistance Rth. When it's connected to some load resistance R, the two resistances will form a voltage divider for the Thevenin voltage source and the voltage across the load will thus be
[tex] Vo = V_{th} \frac{R}{R + R_{th}}[/tex]

Now, if you stick a resistance R onto your circuit on the right as a load, you should be able to apply nodal analysis at the output node and solve for Vo. One equation! If you can then put the result in the form above you can read off both the Thevenin voltage and resistance directly.

 

Solve for Vo with the dependent source in place, of course. You'll be finding the expression for the current Ix through the 1000Ω resistor as part of the node equation analysis, so you can substitute for Ix/2 easily.