1. **State the problem:** Solve the equation $$2 - \frac{x + 3}{4} = \frac{x - 1}{8}$$ for $x$. 2. **Identify the formula and rules:** To solve equations with fractions, multiply both sides by the least common denominator (LCD) to eliminate fractions. 3. **Find the LCD:** The denominators are 4 and 8, so the LCD is 8. 4. **Multiply both sides by 8:** $$8 \times \left(2 - \frac{x + 3}{4}\right) = 8 \times \frac{x - 1}{8}$$ 5. **Distribute multiplication:** $$8 \times 2 - 8 \times \frac{x + 3}{4} = \cancel{8} \times \frac{x - 1}{\cancel{8}}$$ $$16 - 2(x + 3) = x - 1$$ 6. **Distribute $-2$ on the left side:** $$16 - 2x - 6 = x - 1$$ 7. **Simplify left side:** $$10 - 2x = x - 1$$ 8. **Add $2x$ to both sides:** $$10 - \cancel{2x} + 2x = x - 1 + 2x$$ $$10 = 3x - 1$$ 9. **Add 1 to both sides:** $$10 + 1 = 3x - 1 + 1$$ $$11 = 3x$$ 10. **Divide both sides by 3:** $$\frac{11}{\cancel{3}} = \frac{3x}{\cancel{3}}$$ $$x = \frac{11}{3}$$ **Final answer:** $$x = \frac{11}{3}$$