$4 - (\frac{41}{84} - \frac{5}{21}) + 7\frac{11}{30} = 4 - (\frac{41}{84} - \frac{20}{84}) + 7\frac{11}{30} = 4 - \frac{21}{84} + 7\frac{11}{30} = 4 - \frac{1}{4} + 7\frac{11}{30} = 3\frac{3}{4} + 7\frac{11}{30} = 3\frac{45}{60} + 7\frac{22}{60} = 10\frac{67}{60} = 11\frac{7}{60}$