What number complete the pattern? Note that there is a single algebraic equations(limited to the basic arithmetic operations of addition, subtraction, multiplication and division) that can repeats across all rows.  6,-5,-6,5.                                                    -4,3,2,-6.                                                      6,6,9,4.                                                         -9,?,6,3

To find the missing number in the sequence, we need to determine a consistent algebraic pattern that applies to each row. Let's investigate the pattern row by row:

**First row**:  
\( 6, -5, -6, 5 \)  
We observe an alternating sign pattern, but we are looking for an algebraic relationship.

**Second row**:  
\( -4, 3, 2, -6 \)

**Third row**:  
\( 6, 6, 9, 4 \)

Now, let's try to figure out an algebraic relationship that applies consistently across all rows using basic operations.

### Investigating a Potential Equation
1. **First column:**
   - \( 6 \), \( -4 \), \( 6 \), \( -9 \)

2. **Second column:**
   - \( -5 \), \( 3 \), \( 6 \), \( ? \)

3. **Third column:**
   - \( -6 \), \( 2 \), \( 9 \), \( 6 \)

4. **Fourth column:**
   - \( 5 \), \( -6 \), \( 4 \), \( 3 \)

### Trying Addition/Subtraction Patterns:
Look for a consistent difference:
- **First and second column difference:**  
\( 6 - (-5) = 11 \)  
\( -4 - 3 = -7 \)  
\( 6 - 6 = 0 \)

- **Third and fourth column difference:**  
\( -6 - 5 = -11 \)  
\( 2 - (-6) = 8 \)  
\( 9 - 4 = 5 \)

There seems to be no simple additive pattern. 

### Trying Multiplication Patterns:
Let's attempt a ratio approach.

What number completes the pattern? Note that there is a single algebraic equation (limited to the basic arithmetic operations of addition, subtraction, multiplication, and division) that repeats across all rows. 6, -5, -6, 5. -4, 3, 2, -6. 6, 6, 9, 4. -9, ?, 6, 3

In this problem, we investigate an algebraic sequence pattern across multiple rows to find the missing number. The solution involves identifying arithmetic relationships through addition, subtraction, and multiplication. Suitable for students in Grades 6-8.

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