1. **State the problem:** Solve the equation $$\frac{3x}{5} = 2x - \frac{9}{5}$$ for $x$. 2. **Write down the equation:** $$\frac{3x}{5} = 2x - \frac{9}{5}$$ 3. **Eliminate the denominators:** Multiply both sides of the equation by 5 to clear the fractions: $$5 \times \frac{3x}{5} = 5 \times \left(2x - \frac{9}{5}\right)$$ which simplifies to $$3x = 10x - 9$$ 4. **Isolate the variable terms:** Subtract $10x$ from both sides: $$3x - 10x = -9$$ which simplifies to $$-7x = -9$$ 5. **Solve for $x$:** Divide both sides by $-7$: $$x = \frac{-9}{-7} = \frac{9}{7}$$ 6. **Final answer:** $$x = \frac{9}{7}$$