Hello, I've been having difficulty dealting with circuit analysis.

Here, for example, I'm given the task to find the voltage on Vs. But I fail short half-way through.

My attempt at solving this:

V(R5)=4 V because parallel to that thing

I(R4)=4V/1k=4mA=I(R3)

2k=V(R4)/4mA => V(R4)=2k*4m=8 V

Then I applied mesh equation to last mesh:

V(IA)+8V+4V=0 <=> V(IA)=-12 V (How?)

Node equation at a:

2mA=4mA+I(R3) => I(R3)=-2mA (What does this mean?)

V(R3)=3k*(-2mA)=-6 V

Mesh on middle:

-12V-(-6V)-(-6V)+V(R2)=0

V(R2)=0 Impossible

Please help me understand what I did wrong,

Here, for example, I'm given the task to find the voltage on Vs. But I fail short half-way through.

__Also, I don't understand how to deal with negative voltages and/or currents, and would appreciate help!__My attempt at solving this:

V(R5)=4 V because parallel to that thing

I(R4)=4V/1k=4mA=I(R3)

2k=V(R4)/4mA => V(R4)=2k*4m=8 V

Then I applied mesh equation to last mesh:

V(IA)+8V+4V=0 <=> V(IA)=-12 V (How?)

Node equation at a:

2mA=4mA+I(R3) => I(R3)=-2mA (What does this mean?)

V(R3)=3k*(-2mA)=-6 V

Mesh on middle:

-12V-(-6V)-(-6V)+V(R2)=0

V(R2)=0 Impossible

Please help me understand what I did wrong,

__and consider as if I was very dumb (which is probably true).__
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