An ideal gas did work equal to 100 J and gave off an amount of heat equal to 300 J, how did the internal energy change?

To solve the problem, you need to remember the first law of thermodynamics:
the internal energy of an ideal gas depends on the amount of heat and work that is performed and is measured by the difference between these two quantities.
The first law of thermodynamics is:
ΔU = Q – A. ΔU = – 300 J – 100 J = – 400 J.
Answer: the internal energy of an ideal gas decreased by 400 J.