Your question is confusing, and it seems to get more so each time you add a "clarification"!
You've labelled your diagram with two currents. One, i
x, seems to be associated with the 6Ω resistor branch. But then you say it's associated with the "unknown voltage source", presumably Vx. But you've also labelled the current coming from Vx with a value of what appears to be 13A. Then you say that I is ix and that ix = 3A

Adding to the mystery is that you've written three equations without describing what they are meant to represent, with sequences like " +18 -5 - 5" that are hard to fathom from the given diagram, since no particular current or resistor values are specified to let us know what path is being followed through the circuit.
In your problem statement you ask, "What is the value of R?". But there is no component labelled "R" on the diagram; Only one labelled R
A seems to be an unknown.
Furthermore, since the 6Ω resistor is paralleled by the 18V supply the current through it cannot be anything but 3A, so being given its value (i
x) doesn't add any information. And R
A is also paralleled by the 18V supply, so unless you know more about the currents supplied or absorbed by
both voltage supplies, it doesn't look hopeful for finding a particular value for R
A.