Problem inspired from thermodynamics

[Bipolarity]

Homework Statement

While studying thermodynamics, I constructed the following problem, which I can't seem to solve.

Suppose that $Q_{4} > Q_{3}$ and $|Q_{3}| > |Q_{4}|$. Then for what values of ΔU is it necessarily the case that $|ΔU-Q_{4}| > |ΔU-Q_{3}|$

Homework Equations

The Attempt at a Solution

I really have no idea what to do; I solved a much simpler textbook style problem and then decided to consider a more general version of the problem, which led me to this. Any ideas? I conjecture that both the Q values are negative, but is this true? How would I prove it?

BiP

 

[haruspex]

Certainly Q₃ < 0, but Q₄ need only be smaller in magnitude. You could draw up a truth table to see this, and similarly to deduce the range of ΔU.