1. **State the problem:** When 14 is subtracted from half of the number $k$, the result is at most 18. 2. **Translate the problem into an inequality:** Half of the number $k$ is $\frac{k}{2}$. Subtracting 14 from this gives $\frac{k}{2} - 14$. The phrase "at most 18" means less than or equal to 18. So, the inequality is: $$\frac{k}{2} - 14 \leq 18$$ 3. **Solve the inequality:** Add 14 to both sides: $$\frac{k}{2} \leq 18 + 14$$ $$\frac{k}{2} \leq 32$$ Multiply both sides by 2 to solve for $k$: $$k \leq 64$$ 4. **Interpretation:** The number $k$ must be less than or equal to 64 to satisfy the condition. **Final answer:** $$k \leq 64$$