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**Math Problems Identified:**

The image contains three math problems under the category of absolute values:

1. \( 7x - 9 = 4 \)
2. \( 7x + 4 = 6x + 9 \)
3. \( -6(3x + 1) = 2(3 - 9x) - 3 \)

### Problem 1: \( 7x - 9 = 4 \)

**Solution:**
1. Add 9 to both sides: 
   \[
   7x - 9 + 9 = 4 + 9
   \]
   Simplifies to:
   \[
   7x = 13
   \]
2. Divide both sides by 7:
   \[
   x = \frac{13}{7}
   \]

### Problem 2: \( 7x + 4 = 6x + 9 \)

**Solution:**
1. Subtract \( 6x \) from both sides:
   \[
   7x - 6x + 4 = 9
   \]
   Simplifies to:
   \[
   x + 4 = 9
   \]
2. Subtract 4 from both sides:
   \[
   x = 5
   \]

### Problem 3: \( -6(3x + 1) = 2(3 - 9x) - 3 \)

**Solution:**
1. Distribute the multiplication on both sides:
   \[
   -18x - 6 = 6 - 18x - 3
   \]
   Simplifies to:
   \[
   -18x - 6 = 3 - 18x
   \]
2. Add \( 18x \) to both sides:
   \[
   0 - 6 = 3
   \]
   Which simplifies to a contradiction:
   Therefore, no solution exists.

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Would you like further details on any of the problems?

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**Questions:**
1. What is the importance of checking for contradictions in equations?
2. How can absolute values affect the solutions of linear equations?
3. What other methods could be used to solve linear equations?
4. Why is it important to simplify equations early in the process?
5. How does distributing multiplication across parentheses work in algebra?

**Tip:** Always simplify the equation step by step to avoid confusion and errors.

The user uploaded an image containing three mathematical problems related to algebra and absolute values.

Explore detailed solutions to algebraic equations involving absolute values. Learn how to solve problems like 7x - 9 = 4, 7x + 4 = 6x + 9, and others, with step-by-step explanations. Suitable for students in Grades 9-10.

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