If we added heat (Q) to the, and we knew this resulted in an increase of internal energy (U) of + 15, what would the change in work (W) have to be in order for the equation to balance.

The question is incomplete, here is the complete question:

If we added 10 J of heat (Q) to the system, and we knew this resulted in an increase of internal energy (U) of +15 J, what would the change in work have to be in order for the equation to balance.

The work done for compression is +5 J

Explanation:

According to first law of thermodynamics:

where,

q = heat released or absorbed = +10 J  

When heat is added, it is getting absorbed and sign will be positive and when heat is removed, it is getting released and sign will be negative

dU = internal energy = +15 J

W = work done

Putting values in above equation, we get:

Sign convention of work:

Work done for expansion process is taken as negative and work done for compression is taken as positive.

Hence, the work done for compression is +5 J

the answer would be b i believe