Let's break down the problem step-by-step:

1. A number $u$ is decreased by 8. This gives us: $u - 8$.
2. The result is then multiplied by 3. This gives: $3(u - 8)$.
3. The final result is greater than the original number $u$. This gives the inequality: $3(u - 8) > u$

Now, let's solve this inequality:

$3(u - 8) > u$ Expand the left side: $3u - 24 > u$ Subtract $u$ from both sides: $2u - 24 > 0$ Add 24 to both sides: $2u > 24$ Divide both sides by 2: $u > 12$

Final Answer:

The inequality is $u > 12$, meaning the possible values for $u$ are any numbers greater than 12.

Would you like more details on this solution or have any questions? Here are 5 related questions to explore:

1. What happens if the final result was less than the original number?
2. How would the inequality change if we added 8 to the number instead of subtracting?
3. Can you graph the solution of $u > 12$ on a number line?
4. How do we write and solve inequalities with two variables?
5. What are some real-world applications of solving inequalities?

Tip: Always verify your solution by substituting values of $u$ to see if they satisfy the original inequality!