1. **State the problem:** Solve the equation $$\frac{2}{3}x = 10$$ for $x$. 2. **Formula and rules:** To solve for $x$, we need to isolate $x$ by dividing both sides of the equation by the coefficient of $x$, which is $\frac{2}{3}$. 3. **Isolate $x$:** $$x = \frac{10}{\frac{2}{3}}$$ 4. **Divide by a fraction:** Dividing by a fraction is the same as multiplying by its reciprocal: $$x = 10 \times \frac{3}{2}$$ 5. **Multiply:** $$x = \frac{10 \times 3}{2} = \frac{30}{2}$$ 6. **Simplify:** $$x = 15$$ **Final answer:** $$x = 15$$