1. **State the problem:** Solve the equation $$3 - 2x = \frac{3}{4}(x + 3)$$. 2. **Distribute the right side:** Apply the distributive property to expand $$\frac{3}{4}(x + 3)$$: $$3 - 2x = \frac{3}{4}x + \frac{3}{4} \times 3$$ $$3 - 2x = \frac{3}{4}x + \frac{9}{4}$$ 3. **Move all terms involving $$x$$ to one side and constants to the other:** Subtract $$\frac{3}{4}x$$ from both sides and subtract 3 from both sides: $$3 - 2x - \frac{3}{4}x = \frac{9}{4}$$ $$3 - 3 = \frac{9}{4} + 2x - \frac{3}{4}x$$ Simplify left side: $$0 = \frac{9}{4} + 2x - \frac{3}{4}x$$ 4. **Combine like terms on the right side:** $$2x - \frac{3}{4}x = \frac{8}{4}x - \frac{3}{4}x = \frac{5}{4}x$$ So, $$0 = \frac{9}{4} + \frac{5}{4}x$$ 5. **Isolate $$x$$:** Subtract $$\frac{9}{4}$$ from both sides: $$-\frac{9}{4} = \frac{5}{4}x$$ 6. **Divide both sides by $$\frac{5}{4}$$ to solve for $$x$$:** $$x = \frac{-\frac{9}{4}}{\frac{5}{4}}$$ Show cancellation: $$x = -\frac{9}{4} \times \frac{4}{5} = -\frac{9}{\cancel{4}} \times \frac{\cancel{4}}{5} = -\frac{9}{5}$$ 7. **Final answer:** $$\boxed{x = -\frac{9}{5}}$$ This means the solution to the equation is $$x = -1.8$$.