I struggle grasping circuits, especially Op-Amps. In my research, I was able to put together this inverting op-amp circuit in LTSpice that takes the input and level shifts it by +1.5V. I understand it has a lot to do with the voltage divider located at the non-inverting input, but I cannot fully understand why. This voltage divider turns the 5V to 0.75V and I could see by doubling that, it becomes 1.5V and the shift that I want appears. I believe there is a greater mathematical significance here than simply that. Leaving R1 and R2 equal means the gain will be 1(or -1?), so I'm happy so far.
However, if I wanted to alter the values of R1 and/or R2 to add in gain, the gain appears in the simulation, but my +1.5V shift changes. I understand this change is possibly due to the summing of voltage at the op-amp's inputs, and by changing the resistors R1 or R2, I am changing the math of the entire system. I don't know what that has to do with the level shift though. I can change the shift and not the gain, but I can't change the gain without also changing the shift.
Additionally, if I wanted to provide a gain of 2(or a gain at all) in addition to this +1.5V level shift, how can I figure that out? Would it be better to separate my goals here by creating two op-amp circuits that achieve both individually?
Also, for clarification, the green wave is the signal at the sine wave voltage input. The blue wave is the output "Vout."