The statement in question is:
"The distance from zero is called Absolute Value."
To determine whether this statement is true or false, let's break down the key concepts:
1. Absolute Value Definition: The absolute value of a number is defined as its distance from zero on the number line, regardless of direction. For example, whether a number is positive or negative, its absolute value will always be non-negative.
2. Mathematical Representation: If [tex]\( x \)[/tex] is a real number, the absolute value of [tex]\( x \)[/tex] is denoted by [tex]\( |x| \)[/tex]. This can be formally described as:
- [tex]\( |x| = x \)[/tex] if [tex]\( x \geq 0 \)[/tex]
- [tex]\( |x| = -x \)[/tex] if [tex]\( x < 0 \)[/tex]
3. Examples:
- [tex]\( |3| = 3 \)[/tex]
- [tex]\( |-3| = 3 \)[/tex]
- [tex]\( |0| = 0 \)[/tex]
From these points, it is clear that the absolute value of a number does represent its distance from zero on the number line.
Therefore, the statement is indeed true.
Conclusion: True
