1. **State the problem:** Solve the equation $1 + 7(-7k + 5) = -111$ for $k$. 2. **Apply the distributive property:** Multiply 7 by each term inside the parentheses: $$1 + 7 \times (-7k) + 7 \times 5 = 1 - 49k + 35$$ 3. **Simplify the left side:** $$1 - 49k + 35 = 36 - 49k$$ 4. **Rewrite the equation:** $$36 - 49k = -111$$ 5. **Isolate the term with $k$:** Subtract 36 from both sides: $$36 - 49k - 36 = -111 - 36$$ $$\cancel{36} - 49k - \cancel{36} = -147$$ $$-49k = -147$$ 6. **Solve for $k$:** Divide both sides by $-49$: $$\frac{-49k}{-49} = \frac{-147}{-49}$$ $$\cancel{-49}k / \cancel{-49} = 3$$ $$k = 3$$ **Final answer:** $k = 3$