1. **State the problem:** Samuel thinks of a number $k$. He triples it and then subtracts 11 to get a result less than 43. 2. **Write the inequality:** Tripling $k$ means $3k$. Subtracting 11 gives $3k - 11$. The result is less than 43, so the inequality is: $$3k - 11 < 43$$ 3. **Solve the inequality:** Add 11 to both sides: $$3k - 11 + 11 < 43 + 11$$ $$3k < 54$$ Divide both sides by 3: $$\frac{\cancel{3}k}{\cancel{3}} < \frac{54}{3}$$ $$k < 18$$ 4. **Interpretation:** The possible values of $k$ are all real numbers less than 18. **Final answer:** $$k < 18$$