1. **State the problem:** Solve the equation $$\frac{2}{3}2x - \frac{1}{3} = x = 3$$ for $x$. 2. **Clarify the equation:** The expression seems ambiguous. Assuming the problem is to solve $$\frac{2}{3} \cdot 2x - \frac{1}{3} = 3$$ for $x$. 3. **Write the equation:** $$\frac{2}{3} \times 2x - \frac{1}{3} = 3$$ 4. **Simplify the left side:** $$\frac{2}{3} \times 2x = \frac{4x}{3}$$ so the equation becomes $$\frac{4x}{3} - \frac{1}{3} = 3$$ 5. **Add $\frac{1}{3}$ to both sides:** $$\frac{4x}{3} = 3 + \frac{1}{3}$$ 6. **Convert 3 to a fraction with denominator 3:** $$3 = \frac{9}{3}$$ so $$\frac{4x}{3} = \frac{9}{3} + \frac{1}{3} = \frac{10}{3}$$ 7. **Multiply both sides by 3 to clear denominators:** $$4x = 10$$ 8. **Divide both sides by 4:** $$x = \frac{10}{4} = \frac{5}{2}$$ **Final answer:** $$x = \frac{5}{2}$$