1. **State the problem:** Solve the equation $$\frac{3}{4} - \frac{1}{2}b = -3b$$ for $b$. 2. **Rewrite the equation:** We want to isolate $b$. The equation is $$\frac{3}{4} - \frac{1}{2}b = -3b$$. 3. **Add $\frac{1}{2}b$ to both sides to get all $b$ terms on one side:** $$\frac{3}{4} = -3b + \frac{1}{2}b$$ 4. **Combine like terms on the right side:** $$-3b + \frac{1}{2}b = \left(-3 + \frac{1}{2}\right)b = \left(-\frac{6}{2} + \frac{1}{2}\right)b = -\frac{5}{2}b$$ So the equation becomes: $$\frac{3}{4} = -\frac{5}{2}b$$ 5. **Solve for $b$ by dividing both sides by $-\frac{5}{2}$:** $$b = \frac{\frac{3}{4}}{-\frac{5}{2}}$$ 6. **Simplify the division of fractions:** $$b = \frac{3}{4} \times \frac{\cancel{2}}{\cancel{-5}} \quad \Rightarrow \quad b = \frac{3 \times 2}{4 \times (-5)} = \frac{6}{-20}$$ 7. **Simplify the fraction:** $$b = -\frac{6}{20} = -\frac{3}{10}$$ **Final answer:** $$b = -\frac{3}{10}$$