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### General Rule:

**El producto de dos enteros con signos diferentes es negativo, y el producto de dos enteros con el mismo signo es positivo.**

(Translation: The product of two integers with different signs is negative, and the product of two integers with the same sign is positive.)

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### Examples:

1. **Example 1: Multiplication \(-8 \times 4\)**  
   Solution: \(-8 \times 4 = -32\)  
   Explanation: Multiplying a negative by a positive results in a negative number.

2. **Example 2: Multiplication \(20 \times -7\)**  
   Solution: \(20 \times -7 = -140\)  
   Explanation: Multiplying a positive by a negative results in a negative number.

3. **Example 3: Multiplication \(-9 \times -3\)**  
   Solution: \(-9 \times -3 = 27\)  
   Explanation: Multiplying two negative numbers results in a positive number.

4. **Example 4: Solving the equation \(x = -3 \times -7 + 4 \times -8\)**  
   Step 1: \(-3 \times -7 = 21\)  
   Step 2: \(4 \times -8 = -32\)  
   Final: \(x = 21 + (-32) = -11\)

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### Exercises:

1. **Multiplication Problems:**
   1. \(-5 \times 3\)
   2. \(-14 \times -7\)
   3. \(6 \times -9\)
   4. \(-4 \times -5\)
   5. \(8 \times -7\)
   6. \(-9 \times -3\)

2. **Equation Solving Problems:**
   - \(a = -9\), \(b = -3\), \(c = 4\), solve \(x = a \times b + c \times -8\)
   - Follow similar steps as shown in Example 4.

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The image contains examples and exercises related to multiplication and solving algebraic equations with both positive and negative numbers.

Explore how to multiply integers with different and same signs, and solve algebraic equations involving both positive and negative numbers. This guide includes examples and exercises, suitable for students in Grades 6-8.

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