1. **State the problem:** Solve the equation $$\frac{2x + 1}{4} + \frac{6x + 2}{5} = \frac{1}{4}$$ to find the value of $x$. 2. **Identify the formula and rules:** To solve equations with fractions, find a common denominator to clear the fractions by multiplying both sides of the equation. 3. **Find the least common denominator (LCD):** The denominators are 4, 5, and 4. The LCD is 20. 4. **Multiply every term by 20 to clear denominators:** $$20 \times \frac{2x + 1}{4} + 20 \times \frac{6x + 2}{5} = 20 \times \frac{1}{4}$$ 5. **Simplify each term:** $$5(2x + 1) + 4(6x + 2) = 5$$ 6. **Distribute:** $$10x + 5 + 24x + 8 = 5$$ 7. **Combine like terms:** $$34x + 13 = 5$$ 8. **Isolate $x$:** $$34x = 5 - 13$$ $$34x = -8$$ 9. **Solve for $x$:** $$x = \frac{-8}{34} = \frac{-4}{17}$$ **Final answer:** $x = \frac{-4}{17}$ which corresponds to option b).