Op amp outside resistive network
I'm not sure where you're going with all the maths but the following may help. Often to get an intuitive feel for the various voltages in an op-amp circuit I tend to think of the circuit in proportional terms or, when looking at a virtual earth point, as a see-saw.



Figure 1. With the values shown in the OP's circuit the voltage at x can be graphically or mentally calculated as 1/3 of the way between 1 V and 10 V. The graph shows this to be 4 V.



Figure 2. The voltage see-saw about the virtual earth on an inverting op-amp.

When given the input voltage, V1, of the inverting op-amp circuit the output can be graphically or mentally calculated by using a see-saw or lever about the 0 V point with the lever arm lengths being in the same ratio as the resistor values.*

I hope that help.

Images: original.