1. **State the problem:** Solve the equation $$\frac{x+2}{3} - \frac{1}{2} = 2$$. 2. **Formula and rules:** To solve equations with fractions, find a common denominator to eliminate fractions by multiplying both sides. 3. **Find the least common denominator (LCD):** The denominators are 3 and 2, so $$\text{LCD} = 6$$. 4. **Multiply both sides by 6:** $$6 \times \left(\frac{x+2}{3} - \frac{1}{2}\right) = 6 \times 2$$ 5. **Distribute multiplication:** $$6 \times \frac{x+2}{3} - 6 \times \frac{1}{2} = 12$$ 6. **Simplify each term:** $$\cancel{6} \times \frac{x+2}{\cancel{3}} = 2(x+2)$$ $$\cancel{6} \times \frac{1}{\cancel{2}} = 3$$ So the equation becomes: $$2(x+2) - 3 = 12$$ 7. **Expand and simplify:** $$2x + 4 - 3 = 12$$ $$2x + 1 = 12$$ 8. **Isolate $x$:** $$2x = 12 - 1$$ $$2x = 11$$ 9. **Divide both sides by 2:** $$\frac{2x}{\cancel{2}} = \frac{11}{\cancel{2}}$$ $$x = \frac{11}{2}$$ **Final answer:** $$x = \frac{11}{2}$$