1. **State the problem:** Solve the equation $$\frac{x}{5} = 11 - 2x$$ for $x$. 2. **Formula and rules:** To solve for $x$, we want to isolate $x$ on one side. We can do this by eliminating fractions and combining like terms. 3. **Eliminate the fraction:** Multiply both sides by 5 to clear the denominator: $$5 \times \frac{x}{5} = 5 \times (11 - 2x)$$ which simplifies to $$x = 55 - 10x$$ 4. **Combine like terms:** Add $10x$ to both sides to get all $x$ terms on one side: $$x + 10x = 55 - 10x + 10x$$ $$11x = 55$$ 5. **Solve for $x$:** Divide both sides by 11: $$\frac{\cancel{11}x}{\cancel{11}} = \frac{55}{11}$$ $$x = 5$$ 6. **Final answer:** The solution to the equation is $$x = 5$$.