1. **State the problem:** Solve the equation $$\frac{y+1}{3} + \frac{y+1}{2} = 2 - \frac{y+3}{2}$$. 2. **Identify the formula and rules:** To solve equations with fractions, find a common denominator to clear 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 to clear denominators:** $$6 \times \left(\frac{y+1}{3} + \frac{y+1}{2}\right) = 6 \times \left(2 - \frac{y+3}{2}\right)$$ 5. **Distribute multiplication:** $$6 \times \frac{y+1}{3} + 6 \times \frac{y+1}{2} = 6 \times 2 - 6 \times \frac{y+3}{2}$$ 6. **Simplify each term:** $$2(y+1) + 3(y+1) = 12 - 3(y+3)$$ 7. **Expand parentheses:** $$2y + 2 + 3y + 3 = 12 - 3y - 9$$ 8. **Combine like terms:** $$5y + 5 = 12 - 3y - 9$$ $$5y + 5 = 3 - 3y$$ 9. **Add $$3y$$ to both sides:** $$5y + 3y + 5 = 3$$ $$8y + 5 = 3$$ 10. **Subtract 5 from both sides:** $$8y = 3 - 5$$ $$8y = -2$$ 11. **Divide both sides by 8:** $$y = \frac{-2}{8} = -\frac{1}{4}$$ **Final answer:** $$y = -\frac{1}{4}$$