1. The problem states: "Eight minus a number $x$ divided by three is greater than or equal to eleven." We need to translate this sentence into an inequality. 2. Let the number be $x$. The phrase "Eight minus a number $x$" translates to $8 - x$. 3. The phrase "divided by three" means we divide the entire expression $8 - x$ by 3, so we write $\frac{8 - x}{3}$. 4. The phrase "is greater than or equal to eleven" translates to $\geq 11$. 5. Putting it all together, the inequality is: $$\frac{8 - x}{3} \geq 11$$ 6. To solve for $x$, multiply both sides by 3 to eliminate the denominator: $$\cancel{3} \times \frac{8 - x}{\cancel{3}} \geq 11 \times 3$$ which simplifies to: $$8 - x \geq 33$$ 7. Next, subtract 8 from both sides: $$8 - x - 8 \geq 33 - 8$$ which simplifies to: $$-x \geq 25$$ 8. Multiply both sides by $-1$ to solve for $x$. Remember to reverse the inequality sign when multiplying by a negative number: $$\cancel{-1} \times (-x) \leq 25 \times \cancel{-1}$$ which simplifies to: $$x \leq -25$$ **Final answer:** $$x \leq -25$$