1. **State the problem:** Solve the equation $\frac{x}{3} = 8 - x$ for $x$. 2. **Formula and rules:** To solve for $x$, we want to isolate $x$ on one side. We can do this by eliminating the fraction and combining like terms. 3. **Multiply both sides by 3 to clear the denominator:** $$3 \times \frac{x}{3} = 3 \times (8 - x)$$ which simplifies to $$\cancel{3} \times \frac{x}{\cancel{3}} = 24 - 3x$$ so $$x = 24 - 3x$$ 4. **Add $3x$ to both sides to get all $x$ terms on one side:** $$x + 3x = 24 - 3x + 3x$$ which simplifies to $$4x = 24$$ 5. **Divide both sides by 4 to solve for $x$:** $$\frac{4x}{4} = \frac{24}{4}$$ which simplifies to $$\cancel{4}x/\cancel{4} = 6$$ so $$x = 6$$ 6. **Final answer:** $$\boxed{6}$$