1. Convert mixed numbers to improper fractions: \(-\frac{17}{5}b - \frac{21}{20}b = -\frac{31}{10} + \frac{9}{5} - \frac{47}{20}\).
2. Combine like terms: \(\frac{-68b - 21b}{20} = \frac{-62 + 36 - 47}{20}\) which simplifies to \(-\frac{89b}{20} = -\frac{73}{20}\).
3. Solve for b: \(-89b = -73\) => \(b = \frac{73}{89}\).