1. **State the problem:** Solve the inequality $$2 - \frac{m}{11} \leq -7$$ and determine the solution set. 2. **Isolate the variable term:** Subtract 2 from both sides: $$2 - \frac{m}{11} - 2 \leq -7 - 2$$ which simplifies to $$- \frac{m}{11} \leq -9$$ 3. **Eliminate the fraction:** Multiply both sides by 11 to clear the denominator: $$11 \times \left(- \frac{m}{11}\right) \leq 11 \times (-9)$$ which gives $$-m \leq -99$$ 4. **Solve for $m$:** Multiply both sides by $-1$ to get $m$ positive. Remember, multiplying an inequality by a negative number reverses the inequality sign: $$\cancel{-1} \times (-m) \geq \cancel{-1} \times (-99)$$ which simplifies to $$m \geq 99$$ 5. **Interpretation:** The solution is all values of $m$ greater than or equal to 99. 6. **Answer choice:** The correct inequality is $$m \geq 99$$ with the number line shaded to the right of 99 including the point 99. **Final answer:** $$m \geq 99$$