Checking for negative feedback in a circuit

[Milotic]

This is the circuit in question.
During lecture, when checking whether this was negative feedback, my instructor said that if the v_out increases, then v- increases as well, which would lead to the next v_out decreasing because v_out = A(v+ - v-). I get how if v- increases the next v_out would decrease and that'd give a negative feedback, but the problem is, I don't understand how v_out increasing (initially) also leads to the v- increasing.

Actually, there was a similar question we went over just before:

Here, my instructor said the same thing; if the v_out increased, then v- also increases, leading to smaller v_out the next time. Here, I thought I understood why: there's a voltage divider from V_s to v_out, where (v- - v_out) = R2 * V_s /(R1+R2). Since none of the resistances nor the voltage source V_s change, if v_out increases, v- would have to increase as well, or that was my understanding. (Is my understanding right?)

However, going back to the circuit for Inverting Summing Amplifier, we don't exactly have a voltage divider, do we? Because the two voltage sources V1 and V2 are in parallel, I don't see how I could combine them (I think you can only combine voltage sources in series). So assuming I'm right in not seeing any voltage dividers in Inverting Summing Amplifier, what makes v- go up as v_out goes up?

 

[alan123hk]

However, going back to the circuit for Inverting Summing Amplifier, we don't exactly have a voltage divider, do we? Because the two voltage sources V1 and V2 are in parallel, I don't see how I could combine them (I think you can only combine voltage sources in series). So assuming I'm right in not seeing any voltage dividers in Inverting Summing Amplifier, what makes v- go up as v_out goes up?

Since it is an inverting summing amplifier, its function is of course to add all the voltages connected to its inverting input terminal through the corresponding resistor, and then perform inverting amplification. Is it not obvious from the wiring diagram?

Next, I think you can try to derive the circuit equation.

 

[Milotic]

@alan123hk well, I must say sometimes I have trouble understanding wiring diagrams right, but after reading your comment I drew things out again this is what I interpreted the inverting summing amplifier's (partial) circuit to be—is this correct? Since V1 and V2 seem to be kind of in series maybe I could add those two voltage sources(?) to have some form of voltage divider, I guess, but I also have the v_out in parallel with V2, which makes me doubt that.

what I thought initially was this below:

also, what do you mean by circuit equation?

 

[alan123hk]

I must say sometimes I have trouble understanding wiring diagrams right, but after reading your comment I drew things out again this is what I interpreted the inverting summing amplifier's (partial) circuit to be—is this correct? Since V1 and V2 seem to be kind of in series maybe I could add those two voltage sources(?) to have some form of voltage divider, I guess, but I also have the v_out in parallel with V2, which makes me doubt that.

Ignore the op amp first. Please see the picture below.

If V1 is now increased, and V2 and V3 remain unchanged, of course V4 will increase. I believe you should agree with this. Now we increase V2 and V3 sequentially, and the other two voltages remain unchanged, which will cause V4 to increase sequentially as V2 and V3 increase. So, isn't this a simple resistor circuit that adds these three voltages together?