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To solve the inequality \( -5x + 6 > -2x + 9 \), we need to isolate \( x \) on one side. Here are the steps:

1. **Rewrite the inequality:**
   \[
   -5x + 6 > -2x + 9
   \]

2. **Move terms involving \( x \) to one side:**  
   Add \( 5x \) to both sides:
   \[
   6 > 3x + 9
   \]

3. **Move constant terms to the other side:**  
   Subtract \( 9 \) from both sides:
   \[
   -3 > 3x
   \]

4. **Isolate \( x \):**  
   Divide both sides by \( 3 \):
   \[
   -1 > x
   \]
   This is the same as:
   \[
   x < -1
   \]

The solution to the inequality is \( x < -1 \), which means \( x \) is all values less than \(-1\).

**Interpret the Answer:**
Now we match this solution to the given number lines:
- The correct answer is **(a)**, where the number line has a filled dot at \(-1\) with an arrow extending to the left, representing \( x < -1 \) (values less than \(-1\)).

Would you like further details or have any questions about the steps?

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### Related Questions:
1. How would the solution change if the inequality were \( -5x + 6 < -2x + 9 \)?
2. What does an open circle versus a closed circle mean on a number line?
3. How do we solve inequalities when dividing by a negative number?
4. How can we represent inequalities on a coordinate plane instead of a number line?
5. How does solving inequalities differ from solving equalities?

### Tip:
Always remember to reverse the inequality symbol when you multiply or divide both sides by a negative number.

Which is the solution to the inequality -5x + 6 > -2x + 9?

Find the solution to the inequality -5x + 6 > -2x + 9, step-by-step, including isolating the variable and understanding the inequality's direction on a number line. Suitable for Grades 7-9.

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