Kayla claims that the absolute value of a number is always greater than the number itself. Which statement about her claim is true?

Kayla is correct. Any positive number is greater than a negative, and absolute value of a number is always positive.
Kayla is correct. The distance between 0 and a number is always more than the number.
Kayla is incorrect. The absolute value of a positive number is negative, and negative numbers are less than positive numbers.
Kayla is incorrect. The absolute value of 0 or a positive number is equal to the number.

1 answer

The correct statement about Kayla's claim is:

Kayla is incorrect. The absolute value of 0 or a positive number is equal to the number.

Here’s why:

  • The absolute value of a number \( x \) is defined as:
    • \( |x| = x \) if \( x \) is positive or zero,
    • \( |x| = -x \) if \( x \) is negative.

So, for positive numbers and zero, the absolute value is equal to the number itself, not greater.

For negative numbers, the absolute value is greater than the number, since it converts the negative number to a positive one.

Thus, it's not accurate to say that the absolute value of a number is always greater than the number itself; it can be equal (when \( x \) is positive or zero) or greater (when \( x \) is negative).