1. Stating the problem: Solve the equation $$\frac{x}{5} = \frac{8}{11}$$ for $x$. 2. Formula and rules: To solve for $x$ in a proportion $\frac{a}{b} = \frac{c}{d}$, we use cross multiplication: $$a \times d = b \times c$$. 3. Applying cross multiplication: $$x \times 11 = 5 \times 8$$ 4. Simplify the right side: $$11x = 40$$ 5. Solve for $x$ by dividing both sides by 11: $$x = \frac{40}{11}$$ 6. Show cancellation step: $$x = \frac{\cancel{40}}{\cancel{11}}$$ (no common factors to cancel, so fraction remains $\frac{40}{11}$). 7. Final answer: $$x = \frac{40}{11}$$ which is approximately 3.636. This completes the solution for the first problem.