1. The problem is to solve the equation $$\frac{2x}{3} = \frac{1}{3}$$ for $x$. 2. To solve for $x$, we use the property that if two fractions are equal and have the same denominator, their numerators must be equal. Here, both sides have denominator 3. 3. Therefore, we set the numerators equal: $$2x = 1$$ 4. Now, solve for $x$ by dividing both sides by 2: $$x = \frac{1}{2}$$ 5. So, the solution to the equation is: $$x = \frac{1}{2}$$