1. **State the problem:** Solve the equation $93 + 2k + 96 = 6(-7k + 3) + 35$ for $k$. 2. **Combine like terms on the left side:** $$93 + 96 + 2k = 189 + 2k$$ 3. **Expand the right side using distributive property:** $$6(-7k + 3) + 35 = 6 \times -7k + 6 \times 3 + 35 = -42k + 18 + 35$$ 4. **Simplify the right side:** $$-42k + 18 + 35 = -42k + 53$$ 5. **Rewrite the equation:** $$189 + 2k = -42k + 53$$ 6. **Add $42k$ to both sides to get all $k$ terms on one side:** $$189 + 2k + 42k = -42k + 42k + 53$$ $$189 + 44k = 53$$ 7. **Subtract 189 from both sides:** $$189 + 44k - 189 = 53 - 189$$ $$44k = -136$$ 8. **Divide both sides by 44 to solve for $k$:** $$k = \frac{-136}{44}$$ 9. **Simplify the fraction by dividing numerator and denominator by 4:** $$k = \frac{\cancel{-136}^{\div 4}}{\cancel{44}^{\div 4}} = \frac{-34}{11}$$ **Final answer:** $$k = -\frac{34}{11}$$