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We are given the following:

1. A number \( v \) is decreased by 10, i.e., \( v - 10 \).
2. This result is then multiplied by 3, giving \( 3(v - 10) \).
3. The final result is greater than the original number \( v \).

The inequality to represent this situation is:
\[
3(v - 10) > v
\]

### Let's solve this inequality step-by-step:

1. Expand the left-hand side:
   \[
   3(v - 10) = 3v - 30
   \]
   So the inequality becomes:
   \[
   3v - 30 > v
   \]

2. Subtract \( v \) from both sides to simplify:
   \[
   3v - v - 30 > 0
   \]
   This simplifies to:
   \[
   2v - 30 > 0
   \]

3. Add 30 to both sides:
   \[
   2v > 30
   \]

4. Divide both sides by 2:
   \[
   v > 15
   \]

### Conclusion:
The inequality shows that \( v \) must be greater than 15. Hence, the possible values that \( v \) could take are those greater than 15.

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Would you like further details or have any questions?

Here are 5 related questions you might find helpful:

1. How do you write an inequality when a result is less than a number instead of greater?
2. What happens when the inequality includes terms like \( v^2 \) (squared terms)?
3. How would the inequality change if the result was less than or equal to the original number?
4. Can you graph the solution of \( v > 15 \) on a number line?
5. How do you solve inequalities when there are fractions involved?

**Tip:** Always isolate the variable step-by-step when solving inequalities, just like with equations. The main difference is paying attention to flipping the inequality sign when multiplying or dividing by a negative number.

A number, v, is decreased by 10 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 v could take.

Learn how to solve the inequality 3(v - 10) > v with a detailed step-by-step solution. This problem involves understanding inequalities, algebraic manipulation, and solving linear inequalities. Suitable for students in Grades 7-9.

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