The boxed definition of absolute value states that |a|=-a if a is a negative number. Explain why |a| is always nonnegative, even though |a|=-a for negative values of a.

Question

08-07-2022
Mathematics

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The boxed definition of absolute value states that |a|=-a if a is a negative number. Explain why |a| is always nonnegative, even though |a|=-a for negative values of a.

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MericB MericB · Answer 1 · 2022-07-08T23:17:43+02:00

Final answer:

Since absolute values determine the distance between the number and the value whether the value is positive or negative. As distance is always positive.

Thus, |a| is always nonnegative, even though |a|=-a for negative values of a.

Step-by-step explanation:

Step 1

It is said that |a| is always nonnegative even though even though |a|=-a for negative values of a.

Step 2

This is because by the definition of an absolute value, any real number inside an absolute value symbol || will always be positive.