1. **State the problem:** Solve and graph the inequality $$10 \geq \frac{m}{10} + 12$$. 2. **Write the inequality:** $$10 \geq \frac{m}{10} + 12$$. 3. **Isolate the variable term:** Subtract 12 from both sides: $$10 - 12 \geq \frac{m}{10} + 12 - 12$$ $$-2 \geq \frac{m}{10}$$ 4. **Multiply both sides by 10 to solve for $m$:** $$10 \times (-2) \geq 10 \times \frac{m}{10}$$ $$-20 \geq m$$ 5. **Rewrite the inequality:** $$m \leq -20$$ 6. **Interpretation:** The solution is all values of $m$ less than or equal to $-20$. 7. **Graphing:** Since the inequality is $m \leq -20$, we use a closed circle at $-20$ and shade to the left. **Final answer:** Option 3: closed circle at -20 with shading to the left.