1. **Problem statement:** Solve the equation $$1 - \frac{y + 5}{3} = \frac{3(y - 1)}{4}$$ for $y$. 2. **Formula and rules:** To solve linear equations with fractions, first eliminate denominators by multiplying both sides by the least common denominator (LCD). Then simplify and isolate the variable. 3. **Step-by-step solution:** - The denominators are 3 and 4, so the LCD is 12. - Multiply both sides by 12: $$12 \times \left(1 - \frac{y + 5}{3}\right) = 12 \times \frac{3(y - 1)}{4}$$ - Distribute multiplication: $$12 \times 1 - 12 \times \frac{y + 5}{3} = 12 \times \frac{3(y - 1)}{4}$$ $$12 - 4(y + 5) = 9(y - 1)$$ - Expand terms: $$12 - 4y - 20 = 9y - 9$$ - Simplify left side: $$-4y - 8 = 9y - 9$$ - Add $4y$ to both sides: $$-8 = 13y - 9$$ - Add 9 to both sides: $$1 = 13y$$ - Divide both sides by 13: $$y = \frac{1}{13}$$ 4. **Answer:** The solution is $$y = \frac{1}{13}$$. This means the value of $y$ that satisfies the original equation is $\frac{1}{13}$.