1. **State the problem:** Solve the inequality $$5(x - 5) + 2x - 7 \geq 3(x - 6) + 11x$$. 2. **Expand both sides:** $$5x - 25 + 2x - 7 \geq 3x - 18 + 11x$$ 3. **Combine like terms:** $$7x - 32 \geq 14x - 18$$ 4. **Bring all terms involving $x$ to one side and constants to the other:** $$7x - 14x \geq -18 + 32$$ 5. **Simplify:** $$-7x \geq 14$$ 6. **Divide both sides by $-7$ and reverse the inequality sign because dividing by a negative number flips the inequality:** $$\cancel{-7}x \geq 14 \implies x \leq \frac{14}{\cancel{-7}} = -2$$ 7. **Final solution:** $$x \leq -2$$ **Answer in interval notation:** $$(-\infty, -2]$$