1. **State the problem:** Solve the equation $$\frac{3x}{5} = 2x - 9$$ for $x$. 2. **Formula and rules:** To solve for $x$, we want to isolate $x$ on one side. We can eliminate the fraction by multiplying both sides by 5. 3. **Multiply both sides by 5:** $$5 \times \frac{3x}{5} = 5 \times (2x - 9)$$ which simplifies to $$3x = 10x - 45$$ 4. **Bring all $x$ terms to one side:** Subtract $10x$ from both sides: $$3x - 10x = -45$$ which simplifies to $$-7x = -45$$ 5. **Solve for $x$:** Divide both sides by $-7$: $$x = \frac{-45}{-7} = \frac{45}{7}$$ 6. **Final answer:** $$x = \frac{45}{7}$$ This means the solution to the equation is $x = \frac{45}{7}$, or approximately $6.43$.