1. **State the problem:** Solve the equation $$\frac{4}{3}x = x + 60$$ for $x$. 2. **Formula and rules:** To solve for $x$, we need to isolate $x$ on one side. We will use algebraic manipulation including subtraction and division. 3. **Step 1:** Subtract $x$ from both sides to get all $x$ terms on one side: $$\frac{4}{3}x - x = 60$$ 4. **Step 2:** Express $x$ as $\frac{3}{3}x$ to combine like terms: $$\frac{4}{3}x - \frac{3}{3}x = 60$$ 5. **Step 3:** Simplify the left side: $$\left(\frac{4}{3} - \frac{3}{3}\right)x = 60$$ $$\frac{1}{3}x = 60$$ 6. **Step 4:** Multiply both sides by 3 to solve for $x$: $$\cancel{\frac{1}{3}}x \times 3 = 60 \times 3$$ $$x = 180$$ 7. **Final answer:** The solution is $$x = 180$$.