Question

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.

Answer 1

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.

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.