Final answer:
Delta E is negative when a system gives off heat and performs work on its surroundings, as both actions result in energy transfer out of the system, leading to a decrease in internal energy.
Step-by-step explanation:
When a system gives off heat and does work on its surroundings, delta E (change in internal energy) is always negative. This is because, by convention, both heat flow and work have a negative sign when energy is transferred from a system to its surroundings.
Therefore, if a system is releasing heat (d) and doing work (b), it means energy is being transferred out of the system, leading to a decrease in the system's internal energy. Specifically, when a system gives off heat (heat out of the system), it is represented by a negative q value.