1. **State the problem:** Solve the inequality $$\frac{x - 11}{2} > 3x + 5.5$$ for $x$. 2. **Write down the inequality:** $$\frac{x - 11}{2} > 3x + 5.5$$ 3. **Eliminate the fraction by multiplying both sides by 2:** $$\cancel{2} \times \frac{x - 11}{\cancel{2}} > 2 \times (3x + 5.5)$$ $$x - 11 > 6x + 11$$ 4. **Bring all terms involving $x$ to one side and constants to the other:** $$x - 6x > 11 + 11$$ $$-5x > 22$$ 5. **Divide both sides by $-5$ to solve for $x$. Remember, dividing by a negative number reverses the inequality sign:** $$\frac{-5x}{\cancel{-5}} < \frac{22}{\cancel{-5}}$$ $$x < -\frac{22}{5}$$ 6. **Final answer:** $$x < -\frac{22}{5}$$ This corresponds to option ⓐ. **Explanation:** When multiplying or dividing an inequality by a negative number, the inequality sign flips. Here, dividing by $-5$ changed $>$ to $<$.