1. **State the problem:** Solve for $x$ in the equation $11 \times 10^3 = x^3$. 2. **Write the equation:** $$11 \times 10^3 = x^3$$ 3. **Simplify the left side:** $$11 \times 10^3 = 11 \times 1000 = 11000$$ 4. **Rewrite the equation:** $$11000 = x^3$$ 5. **To find $x$, take the cube root of both sides:** $$x = \sqrt[3]{11000}$$ 6. **Calculate the cube root:** Since $22^3 = 10648$ and $23^3 = 12167$, $x$ is between 22 and 23. Using a calculator or approximation: $$x \approx 22.22$$ **Final answer:** $$x \approx 22.22$$