1. **State the problem:** Solve the equation $4(11x - 26) = 4 - 4(x + 5)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by 4. $$4 \times 11x - 4 \times 26 = 4 - 4 \times x - 4 \times 5$$ which simplifies to $$44x - 104 = 4 - 4x - 20$$ 3. **Simplify the right side:** Combine like terms on the right. $$44x - 104 = 4 - 20 - 4x$$ $$44x - 104 = -16 - 4x$$ 4. **Add $4x$ to both sides to get all $x$ terms on one side:** $$44x + 4x - 104 = -16 - 4x + 4x$$ $$48x - 104 = -16$$ 5. **Add 104 to both sides to isolate the $x$ term:** $$48x - 104 + 104 = -16 + 104$$ $$48x = 88$$ 6. **Divide both sides by 48 to solve for $x$:** $$x = \frac{88}{48}$$ Show cancellation of common factors: $$x = \frac{\cancel{88}^{\div 8}}{\cancel{48}^{\div 8}} = \frac{11}{6}$$ **Final answer:** $$x = \frac{11}{6}$$