We are given the inequality:

\[
-6v + 3 \leq -9v - 4
\]

### Steps to solve:

1. **Move all terms involving \(v\) to one side**:
   Add \(9v\) to both sides to eliminate the \(v\) on the right-hand side:
   \[
   -6v + 9v + 3 \leq -4
   \]
   This simplifies to:
   \[
   3v + 3 \leq -4
   \]

2. **Isolate the term involving \(v\)**:
   Subtract 3 from both sides:
   \[
   3v \leq -4 - 3
   \]
   Simplifies to:
   \[
   3v \leq -7
   \]

3. **Solve for \(v\)**:
   Divide both sides by 3:
   \[
   v \leq \frac{-7}{3}
   \]
   So the solution is:
   \[
   v \leq -\frac{7}{3}
   \]

### Final answer:
\[
v \leq -\frac{7}{3}
\]

Would you like a deeper explanation, or do you have any questions?

Here are 5 related questions you might find useful:
1. How do you solve a linear inequality with fractions?
2. What happens if you multiply or divide an inequality by a negative number?
3. Can inequalities have multiple solutions?
4. How do you graph the solution to an inequality on a number line?
5. What are the differences between solving an equation and an inequality?

**Tip**: When solving inequalities, remember that multiplying or dividing by a negative number reverses the inequality sign!

Learn how to solve the linear inequality −6v + 3 ≤ −9v − 4 using step-by-step methods. This solution covers key algebraic concepts, including isolating terms and solving inequalities. Suitable for students in Grades 7-10.

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