1. **State the problem:** Solve the inequality $$7 + 3k \geq 2k - 5$$ and graph the solution set on a number line. 2. **Write down the inequality:** $$7 + 3k \geq 2k - 5$$ 3. **Isolate the variable terms on one side:** Subtract $$2k$$ from both sides: $$7 + 3k - 2k \geq 2k - 5 - 2k$$ which simplifies to $$7 + k \geq -5$$ 4. **Isolate $$k$$:** Subtract 7 from both sides: $$7 + k - 7 \geq -5 - 7$$ which simplifies to $$k \geq -12$$ 5. **Interpretation:** The solution set includes all values of $$k$$ greater than or equal to $$-12$$. 6. **Graphing on a number line:** Draw a number line and shade all values from $$-12$$ to positive infinity, including $$-12$$ (closed circle). **Final answer:** $$k \geq -12$$