https://file.aiquickdraw.com/mathbot/file/17264948565169m5qffi2.jpg

The proof you provided has 3 errors, and the task is to identify each incorrect step and correct them. Let's go through the steps one by one.

### Analysis:

**1. Statement:**
- \( M \) is the midpoint of \( AB \) (Given).
- Reason: Definition of midpoint — This is correct.

**2. Statement:**
- \( AM = MB \).
- Reason: Definition of midpoint — This is also correct as it's a direct consequence of the midpoint definition.

**3. Statement:**
- \( 3x + 7 = 5x - 9 \).
- Reason: Transitive Property — This is incorrect. 

   **Correction:**  
   This step should state that \( AM = 3x + 7 \) and \( MB = 5x - 9 \), and they are equal because \( M \) is the midpoint of \( AB \). Therefore, the reason should be **"Substitution"** (from step 2).

**4. Statement:**
- \( 7 = 2x - 9 \).
- Reason: Subtraction — This is correct because subtracting \( 3x \) from both sides of \( 3x + 7 = 5x - 9 \) yields this equation.

**5. Statement:**
- \( 16 = 2x \).
- Reason: Addition — This is correct because adding 9 to both sides of \( 7 = 2x - 9 \) yields \( 16 = 2x \).

**6. Statement:**
- \( 8 = x \).
- Reason: Division — This is correct because dividing both sides of \( 16 = 2x \) by 2 yields \( 8 = x \).

**7. Statement:**
- \( x = 8 \).
- Reason: Reflexive Property — This is redundant and unnecessary. \( 8 = x \) is already the solution from the previous step. 

   **Correction:**  
   Remove this step entirely or simply state that \( x = 8 \) is the final answer.

### Errors Recap:
1. **Step 3:** The reason should be "Substitution" rather than "Transitive Property".
2. **Step 7:** This step is redundant and should be removed.

Let me know if you want more details or further clarification!

### Related Questions:
1. How do you apply the Substitution Property in proofs like this one?
2. Why is the Transitive Property incorrect in Step 3?
3. Can you explain how to properly simplify equations step by step?
4. What other common errors occur in geometric proofs?
5. What is the difference between Reflexive and Symmetric Properties in geometry?

**Tip:** When working through proofs, always double-check each reason to ensure it directly matches the corresponding statement.

Identify and correct the three errors in the provided proof involving a midpoint and algebraic expressions to prove x = 8.

Learn how to identify and correct errors in a mathematical proof involving the definition of a midpoint and solving algebraic equations. This problem covers key concepts in geometry and algebra, suitable for students in Grades 8-10.

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