[Loop Rule Diagram]
The problem is thus: Apply the loop rule to abcdefghia and find the expression which adds to zero. I tried this, but I was not able to get it correct. I know that when crossing a resistor in the same direction as the current, the voltage is negative, but against the current it is positive. When going with the current from a positive to negative terminal, the voltage is negative, whereas from negative to a positive terminal is positive. The opposite applies if going against the current. I do not need a numerical answer, because the loop adds up to zero, but I would want to understand how to properly add up the voltages. I tried this on the first attempt: -"$I_1$$R_1$+$E_1$-$r_1$$I_1$-$R_5$$I_1$-$r_4$$I_1$-$E_4$+$r_3$$I_3$+$E_3$, but I got sign errors. I tried four other sign permutations but I also got errors. I also don't know in what direction the current goes for the b-d or h-j branches, because $I_2$ is not in the given symbols used to input an answer. If someone could walk me through a step-by-step symbolic solution, I would be grateful, because I tried 5 times and could not get the correct answer (the system only allows 10 attempts to any problem).