https://file.aiquickdraw.com/mathbot/file/1727660320345eo4rhsky.jpg

Let's analyze the problem presented in the image:

### Problem Statement:
- The inequality to solve is: \( 9 - 6x > 27 \)
- The task involves solving the inequality, selecting the correct solution, and graphing the result.

### Step-by-Step Solution:
1. **Start by isolating \( x \):**
   \[
   9 - 6x > 27
   \]
2. **Subtract 9 from both sides:**
   \[
   -6x > 18
   \]
3. **Divide both sides by -6.** (Remember, dividing by a negative number reverses the inequality sign):
   \[
   x < -3
   \]

Thus, the solution is \( x < -3 \).

### Answer Selection:
From the image:
- Option A correctly states that the solution is \( x < -3 \), which matches our solution.

### Graphing:
- The correct graph should show an open circle at \( x = -3 \), and the shading should go towards negative infinity (left side). Based on the image, **Option E** is the correct graphical representation of \( x < -3 \).

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Would you like more details or further clarification on this problem?

Here are five related questions for further practice:
1. How would the inequality change if it were \( 9 - 6x \geq 27 \)?
2. What happens when the inequality involves dividing by a positive number?
3. How would you graph \( x \geq -3 \)?
4. How do you solve and graph \( 5x - 4 > 11 \)?
5. What would the solution be if the inequality was \( -6x < 9 \)?

**Tip:** Always remember to reverse the inequality sign when dividing or multiplying by a negative number!

Solve the inequality 9 - 6x > 27 and graph the solution.

This problem involves solving the inequality 9 - 6x > 27 and graphing the result. The solution shows how to isolate x, reverse the inequality when dividing by a negative number, and graph the correct inequality on the number line. Suitable for students in Grades 7-9.

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