https://file.aiquickdraw.com/mathbot/file/1726453808586zbcxatg8.jpg

Let's solve the inequality step by step:

The inequality given is:

\[
-9 + 4x > 23
\]

### Step 1: Add 9 to both sides of the inequality
\[
4x > 23 + 9
\]
\[
4x > 32
\]

### Step 2: Divide both sides by 4 to solve for \( x \)
\[
x > \frac{32}{4}
\]
\[
x > 8
\]

### Solution:
The inequality is \( x > 8 \).

### Step 3: Graphing the Solution

- On the number line, plot an open circle at \( x = 8 \) because the inequality is strictly greater than (no "equal to").
- Shade the region to the right of 8, indicating all values greater than 8.

### Inequality Notation:
The inequality is written as \( x > 8 \).

For the graph:
- Open circle on 8.
- Arrow pointing to the right, covering values greater than 8.

Would you like more details on graphing or other related questions?

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Here are 5 follow-up questions to deepen understanding:

1. How would the graph change if the inequality was \( x \geq 8 \)?
2. What would the solution be if the inequality was \( -9 + 4x < 23 \)?
3. Can you explain why we divide both sides by 4 to solve for \( x \)?
4. How would the result change if the coefficient of \( x \) was negative, say \( -4x \) instead of \( 4x \)?
5. What are the differences between strict inequalities (like \( > \) or \( < \)) and inclusive inequalities (like \( \geq \) or \( \leq \))?

**Tip**: Always pay attention to whether the inequality symbol includes equality (≥, ≤) or not (>, <) when plotting the graph!

-9 + 4x > 23. Solve the inequality and graph the solution.

Learn how to solve the inequality -9 + 4x > 23 step by step and graph the solution on a number line. This algebraic problem is perfect for students in Grades 7-9 and covers key concepts related to solving inequalities.

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