1. **State the problem:** Solve the linear equation $$\frac{1}{2} - \frac{1}{3}x = 1$$. 2. **Rewrite the equation:** The equation is $$\frac{1}{2} - \frac{1}{3}x = 1$$. 3. **Isolate the term with $x$:** Subtract $\frac{1}{2}$ from both sides: $$\frac{1}{2} - \frac{1}{3}x - \frac{1}{2} = 1 - \frac{1}{2}$$ which simplifies to $$- \frac{1}{3}x = \frac{1}{2}$$ 4. **Divide both sides by $-\frac{1}{3}$ to solve for $x$:** $$x = \frac{\frac{1}{2}}{-\frac{1}{3}}$$ 5. **Simplify the division of fractions:** $$x = \frac{1}{2} \times \frac{-3}{1} = -\frac{3}{2}$$ 6. **Final answer:** $$x = -\frac{3}{2}$$ This means the value of $x$ that satisfies the equation is $-\frac{3}{2}$.