To the Ineffable All,
Some of you got the right answer and some of you did not. Nodal and mesh methods are powerful, but it is like shooting a fly with a howitzer gun. Why get involved with multiple simultaneous equations or matrices when it is unnecessary? I will use the combination Thevenin/Norton theorem, and you all judge whether is is simpler and easier.
Calculate the voltage across Rx when its value is changed to infinity (35 volts). Calculate the current present in Rx when its value is change to zero (7/3 amps). The Thevenin resistance is thereby 35/(7/3) = 15 ohms. Therefore, we are looking at a Thevenin circuit of 35 volts in series with 15 ohms. Now, simply calculate Rx to give a series current of 1.5 amps (35/(15+Rx) = 1.5). Rx is easily found to be 8.33... .
Ratch