Question

Which of the following statements about absolute values and positions on a number line are true? Select each correct answer.

A) Since −7 is 7 units to the left of 0, |−7| = 7.
B) The absolute value of −7 is equal to the absolute value of 7.
C) The absolute value of −7 is negative.
D) −7 is farther to the right on the number line than −8, so |−7| > |−8|.

Answer 1

The absolute value of a number represents its distance from zero on a number line, and it is always a non-negative number. Statements A and B about absolute values are true, while statements C and D are false.

Step-by-step explanation:

The subject in question involves absolute values and their relationship to positions on a number line.

• A) True - The absolute value of a number is the distance of that number from zero on the number line, regardless of direction. So, since −7 is 7 units to the left of 0, |−7| = 7.
• B) True - The absolute value of −7 is 7, which is equal to the absolute value of 7 since they are both 7 units away from zero on the number line.
• C) False - Absolute values are always non-negative. Therefore, the absolute value of −7 cannot be negative.
• D) False - The absolute value of a number is its distance from zero. Both −7 and −8 are equal distances from zero since |−7| = 7 and |−8| = 8, but it is incorrect to say |−7| > |−8| because 7 is not greater than 8.