1. **State the problem:** Solve the equation $$x + \frac{1}{3} = \frac{4}{3}$$. 2. **Formula and rules:** To solve for $x$, we need to isolate $x$ on one side of the equation. This involves subtracting $\frac{1}{3}$ from both sides. 3. **Subtract $\frac{1}{3}$ from both sides:** $$x + \frac{1}{3} - \frac{1}{3} = \frac{4}{3} - \frac{1}{3}$$ 4. **Simplify both sides:** $$x = \frac{4}{3} - \frac{1}{3}$$ 5. **Subtract the fractions:** Since denominators are the same, subtract numerators: $$x = \frac{4 - 1}{3} = \frac{3}{3}$$ 6. **Simplify the fraction:** $$x = 1$$ **Final answer:** $$x = 1$$