1. **State the problem:** Solve the inequality $$\frac{40-k}{5} > 0$$. 2. **Formula and rules:** To solve inequalities involving fractions, multiply both sides by the denominator if it is positive, or multiply and reverse the inequality if the denominator is negative. Here, the denominator is 5, which is positive. 3. **Multiply both sides by 5:** $$\cancel{5} \times \frac{40-k}{\cancel{5}} > 0 \times 5$$ which simplifies to $$40 - k > 0$$. 4. **Isolate $k$:** Subtract 40 from both sides: $$40 - k - 40 > 0 - 40$$ $$-k > -40$$. 5. **Divide both sides by -1:** Remember to reverse the inequality sign when dividing by a negative number: $$\frac{-k}{-1} < \frac{-40}{-1}$$ which simplifies to $$k < 40$$. 6. **Final answer:** The solution to the inequality is $$k < 40$$. This means any value of $k$ less than 40 satisfies the original inequality.