Question

Let x = any negative rational number. Which of the following statements are true?

1) |x| is the opposite of x
2) The absolute value of x is the opposite of x
3) |x| is equal to x
4) The absolute value of x is equal to x
5) |x| is a positive number
6) The absolute value of x is a positive number
7) |x| is greater than x
8) The absolute value of x is greater than x
9) |x| is greater than the distance from 0 to x on the number line

Answer 1

The true statements about the absolute value of a negative rational number x are that the absolute value of x is the opposite of x, |x| is a positive number, the absolute value of x is a positive number, |x| is greater than x, and the absolute value of x is greater than x.

Step-by-step explanation:

Let x be any negative rational number. Given this information, the following statements can be evaluated:

• |x| is the opposite of x - False, since |x| is the absolute value of x, which means it is a positive number, whereas x is negative.
• The absolute value of x is the opposite of x - True, because the absolute value of a negative number is its positive counterpart.
• |x| is equal to x - False, |x| cannot be equal to x because |x| is positive and x is negative.
• The absolute value of x is equal to x - False, for the same reason as above.
• |x| is a positive number - True, as the absolute value of any number is always non-negative.
• The absolute value of x is a positive number - True, this is the definition of absolute value.
• |x| is greater than x - True, because |x| is positive and x is negative.
• The absolute value of x is greater than x - True, for the same reason as above.
• |x| is greater than the distance from 0 to x on the number line - False, the absolute value of x represents that exact distance, so it cannot be greater than itself.

Therefore, the true statements about the absolute value of a negative rational number x are that the absolute value of x is the opposite of x, |x| is a positive number, the absolute value of x is a positive number, |x| is greater than x, and the absolute value of x is greater than x.