Circuit Problem: Find Vx
As you have specifically requested no solution be provided, I will give you only the general strategy for this problem and you can work the rest out yourself.

You will want to apply the 'node voltage' method satisfying KCL for the two 'black dot' nodes drawn in your schematic

As Spehro Pefhany said in his comment, you will want to create an expression relating the 1A current to the voltage across the 'mystery resistor'. This will provide you with a handy substitution that you can use to relate Vx to R with the system of 2 equations you've already built.


To check your answer, I recommend using a SPICE simulator (LTspice and TINA-TI are both free and easy to use).