1. **State the problem:** Solve the equation $$1 - \left(x + \frac{x}{2} + \frac{x}{5}\right) = 20$$ for $x$. 2. **Rewrite the equation:** Combine the terms inside the parentheses: $$x + \frac{x}{2} + \frac{x}{5} = x \left(1 + \frac{1}{2} + \frac{1}{5}\right)$$ 3. **Find a common denominator and sum the fractions:** $$1 + \frac{1}{2} + \frac{1}{5} = \frac{10}{10} + \frac{5}{10} + \frac{2}{10} = \frac{17}{10}$$ 4. **Substitute back:** $$1 - x \cdot \frac{17}{10} = 20$$ 5. **Isolate the term with $x$:** $$- x \cdot \frac{17}{10} = 20 - 1$$ $$- x \cdot \frac{17}{10} = 19$$ 6. **Divide both sides by $-\frac{17}{10}$:** $$x = \frac{19}{-\frac{17}{10}} = 19 \times \frac{10}{-17}$$ 7. **Simplify the multiplication:** $$x = - \frac{190}{17}$$ 8. **Final answer:** $$x = - \frac{190}{17}$$ This means $x$ is approximately $-11.176$.