Textbook Question
Simplify each expression. See Example 8. 3(m - 4) - 2(m + 1)
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0. Review of College Algebra
Solving Linear Equations
1:43 minutesProblem 3
Textbook Question
CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. The opposite, or negative, of a number is its _______.
Verified step by step guidance1
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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Video duration:
1mKey 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.
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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.
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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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