CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. The opposite, or negative, of a number is its _______.

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This problem is about understanding the concept of the opposite, or negative, of a number, which is a fundamental idea in mathematics but not directly a trigonometry problem.

The opposite of a number refers to the value that, when added to the original number, results in zero. This is also known as the additive inverse.

For example, the opposite of a positive number is its negative counterpart, and the opposite of a negative number is its positive counterpart.

In mathematical terms, if the number is \(x\), then its opposite is \(-x\), because \(x + (-x) = 0\).

Therefore, the blank should be filled with the term 'additive inverse' or simply 'additive inverse of the number'.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Opposite (Additive Inverse) of a Number

The opposite of a number, also called its additive inverse, is the number that when added to the original number results in zero. For example, the opposite of 5 is -5 because 5 + (-5) = 0.

Negative of a Number

The negative of a number is the value with the same magnitude but opposite sign. It is essentially the number multiplied by -1. For instance, the negative of 7 is -7.

Number Line Representation

On the number line, the opposite of a number is located the same distance from zero but in the opposite direction. This visual helps understand why opposites have equal magnitude but different signs.

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