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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!

A number, u, is decreased by 8 and the result is then multiplied by 3. The final result is greater than the original number. Write and solve an inequality to show the possible values that u could take.

Learn how to solve an inequality where a number is decreased by 8 and multiplied by 3, with the final result greater than the original number. This problem involves core algebraic concepts and inequalities, suitable for Grades 7-9 students.

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