1. **State the problem:** Solve the equation $$\frac{1}{6}x + \frac{2}{3}x = 1$$ for $x$. 2. **Identify the formula and rules:** To solve for $x$, combine like terms on the left side by finding a common denominator and then isolate $x$. 3. **Find a common denominator:** The denominators are 6 and 3. The least common denominator is 6. 4. **Rewrite the fractions with denominator 6:** $$\frac{1}{6}x + \frac{2}{3}x = \frac{1}{6}x + \frac{2 \times 2}{3 \times 2}x = \frac{1}{6}x + \frac{4}{6}x$$ 5. **Combine the fractions:** $$\frac{1}{6}x + \frac{4}{6}x = \frac{1+4}{6}x = \frac{5}{6}x$$ 6. **Rewrite the equation:** $$\frac{5}{6}x = 1$$ 7. **Isolate $x$ by dividing both sides by $\frac{5}{6}$:** $$x = 1 \div \frac{5}{6} = 1 \times \frac{6}{5}$$ 8. **Show cancellation step:** $$x = \cancel{1} \times \frac{6}{5} = \frac{6}{5}$$ 9. **Final answer:** $$x = \frac{6}{5}$$ This means $x$ equals six-fifths or 1.2.