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The term *additive inverse* refers to a number which, when added to the original number, results in zero. This is a crucial idea in understanding how subtraction can be transformed into addition. Simply put, for any given number, its additive inverse is the number with the opposite sign. This explains the transformation of the subtraction operation into an addition operation. For example:

• The additive inverse of 5 is \(-5\), since \(5 + (-5) = 0\).
• Similarly, the additive inverse of -7 is \(7\), because \(-7 + 7 = 0\).

To work with additive inverses effectively:

• Change the subtraction sign to an addition sign.
• Find the additive inverse of the number that follows the minus sign.

Understanding the concept of additive inverses helps simplify complex expressions and makes operations with integers more intuitive.

*Opposite numbers* are simply numbers that are the same distance away from zero on the number line but in opposite directions. This means, if you have a positive number, its opposite is negative, and vice versa. Opposite numbers are important because they help us perform arithmetic operations like subtraction more easily. For example:

• The opposite of 8 is \(-8\).
• The opposite of \(-3\) is 3.

In the exercise, when we rewrite \(-9 - 5\) as \(-9 + (-5)\), we use the concept of opposite numbers. We take the opposite of 5, which is \(-5\), making subtraction equivalent to adding its opposite. This can be particularly useful when trying to simplify expressions or solve equations involving multiple operations. Recognizing and using opposite numbers becomes a powerful tool in various mathematical contexts.

Understanding *integer operations* is fundamental in solving many mathematical problems, especially when involving negative numbers. When dealing with integer operations, it's essential to know how addition, subtraction, multiplication, and division interact with both positive and negative numbers.

• Addition: When adding two integers with the same sign, add their absolute values and keep the common sign. If different signs, subtract the smaller absolute value from the larger and take the sign of the larger.
• Subtraction: Use the additive inverse to transform subtraction into addition, as seen in the exercise.

For example, if you need to calculate \(-6 - 4\), you can rewrite it as \(-6 + (-4)\). This change stems from recognizing 4 as having its opposite, \(-4\), allowing simpler addition of two negative integers.

• Multiplication and Division: Two numbers with the same sign result in a positive product or quotient, while different signs result in negative.

Mastering integer operations means becoming comfortable with these transformations. They are crucial for building a strong foundation in algebra and beyond.