Finding equivalent resistance

Hi, in example 27, I don't understand how the current through the middle 5 ohm resistor is assumed to be 2x-i, I know that we can use KCL for the junction but it assumes either i-x for the top right 10 ohm resistor or 2x-i for the middle 5 ohm one, how can these assumptions be explained? Is it because of any type of symmetry? Any other way to do these kind of problems? Thank you