Let's solve the given inequality step by step:

Given:
\[
-6v + 5(7v - 4) > -5v + 9 - 2v
\]

### Step 1: Distribute and simplify the terms

Distribute the \(5\) on the left side:
\[
-6v + 35v - 20 > -5v + 9 - 2v
\]

Combine like terms on both sides:
\[
29v - 20 > -7v + 9
\]

### Step 2: Move all terms involving \(v\) to one side

Add \(7v\) to both sides to isolate \(v\) on one side:
\[
29v + 7v - 20 > 9
\]

Simplify:
\[
36v - 20 > 9
\]

### Step 3: Move constant terms to the other side

Add \(20\) to both sides:
\[
36v > 29
\]

### Step 4: Solve for \(v\)

Divide both sides by \(36\):
\[
v > \frac{29}{36}
\]

### Conclusion

The solution to the inequality is:
\[
v > \frac{29}{36}
\]

This means \(v\) must be greater than \(\frac{29}{36}\).

### Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you solve inequalities with parentheses and distributive properties?
2. What are the steps to combine like terms in inequalities?
3. How can you check the solution of an inequality?
4. What happens if you multiply or divide an inequality by a negative number?
5. How do you graph an inequality solution on a number line?

**Tip:** Always ensure that you correctly distribute and combine like terms when solving inequalities.

Learn how to solve the inequality -6v + 5(7v - 4) > -5v + 9 - 2v step-by-step. This problem involves inequalities with parentheses, distributive property, and combining like terms. Suitable for high school students (Grades 9-12).

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