1. **State the problem:** Solve the equation $$x + \frac{3}{5} = \frac{3}{5}$$ for $x$. 2. **Formula and rules:** To isolate $x$, subtract $\frac{3}{5}$ from both sides of the equation. 3. **Subtracting $\frac{3}{5}$ from both sides:** $$x + \frac{3}{5} - \frac{3}{5} = \frac{3}{5} - \frac{3}{5}$$ 4. **Simplify both sides:** $$x + \cancel{\frac{3}{5}} - \cancel{\frac{3}{5}} = \cancel{\frac{3}{5}} - \cancel{\frac{3}{5}}$$ $$x = 0$$ 5. **Conclusion:** The solution to the equation is $x = 0$. This means the value of $x$ that makes the equation true is zero.