First, notice that equation a is just a combination of equations b and c. If you combine b and c you get a:

(equation b) Fe

Fe

^{2+} + 2e

^{-} E

_{2}(equation c) Fe

^{3+} + 3e

^{-} Fe -(E

_{3})

--------------------------------------------------------------------------------------------------------

(equation a) Fe

^{3+} + e

^{-} Fe

^{2+} E

_{1}If you combine a and b you get c:

(equation a) Fe

^{3+} + e

^{-} Fe

^{2+} E

_{1}(equation b) Fe

^{2+} + 2e

^{-} Fe -(E

_{2})

--------------------------------------------------------------------------------------------------------

(equation c) Fe

^{3+} + 3e

^{-} Fe -(E

_{3})

If you combine a and c you get b:

(equation a) Fe

^{3+} + e

^{-} Fe

^{2+} E

_{1}(equation c) Fe

Fe

^{3+} + 3e

^{-} E

_{3}--------------------------------------------------------------------------------------------------------

(equation b) Fe

Fe

^{2+} + 2e

^{-} E

_{2}These relationships all yield the general relationship that E1 = E2 - (E3). Since E1 is positive E2 must be larger than the positive value of E3. This is consistent with your inequality after simplification (E1 + E2 > E1 + E3 > 0 can also be written as simply E2 > E3 > 0 since E1 is added to both E2 and E3).

Now, if we try to add equation a directly to equation b we would get E1 + E2 = E3 which is inconsistent with the relationship E1 = E2 - E3 that appears above. So a + b shouldn't happen directly as written.

However, if we directly add equation a with equation c we would get E1 + E3 = E2 which is consistent with the relationship E1 = E2 - E3 that appears above. Therefore, a + c should be able to happen directly as written (in fact, this is observed if you look at the equations written out in the third example, none of them are "flipped").

I hope this was what you were curious about.