1. **State the problem:** Solve the linear equation $3k + 3 = 33 - 2k$ for $k$. 2. **Write down the equation:** $$3k + 3 = 33 - 2k$$ 3. **Add $2k$ to both sides to get all $k$ terms on one side:** $$3k + 2k + 3 = 33 - \cancel{2k} + 2k$$ $$5k + 3 = 33$$ 4. **Subtract 3 from both sides to isolate the $k$ term:** $$5k + 3 - 3 = 33 - 3$$ $$5k = 30$$ 5. **Divide both sides by 5 to solve for $k$:** $$\frac{5k}{\cancel{5}} = \frac{30}{\cancel{5}}$$ $$k = 6$$ **Final answer:** $k = 6$