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If the absolute value of a nonzero real number is equal to the opposite of the number, the number is __________.

User Bumerang
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Answer:

negative

Explanation:

The absolute value of a number, denoted by |x|, is its distance from zero on the number line without considering direction. For a nonzero real number, let's call it "a," the absolute value is written as |a|.

Now, the statement says that if |a| is equal to the opposite of the number, which is -a, then a must be negative. Mathematically, this is expressed as:

|a| = -a

This scenario occurs when the number a is negative. Let's break it down:

If a is positive, then |a| is equal to a. But in this case, we are saying it's equal to -a.

If a is negative, then |a| is equal to -a. This satisfies the condition stated.

So, when the absolute value of a nonzero real number is equal to the opposite of the number, it implies that the number is negative. It's a subtle yet elegant property of real numbers that underscores the intricacies of mathematical relationships.

User Cjol
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