To solve the question, let's consider the definition of absolute value.
The absolute value of a number is its distance from zero on the number line, regardless of direction. Mathematically, if [tex]\(|x| = 12\)[/tex], it means that [tex]\(x\)[/tex] is 12 units away from zero on the number line. This distance could either be in the positive direction or in the negative direction.
Therefore, we can write the following equation based on the definition of absolute value:
[tex]\[
|x| = 12
\][/tex]
This means:
[tex]\[
x = 12 \quad \text{or} \quad x = -12
\][/tex]
Thus, the number [tex]\(x\)[/tex] can be either [tex]\(12\)[/tex] or [tex]\(-12\)[/tex].
Among the given choices:
- [tex]\(x\)[/tex] is zero: This is incorrect because the absolute value of 0 is 0, not 12.
- [tex]\(x\)[/tex] can be 12 or -12: This is true because both [tex]\(12\)[/tex] and [tex]\(-12\)[/tex] are 12 units away from zero on the number line.
- [tex]\(x = 12\)[/tex]: This statement is partially correct but incomplete, as it does not account for the negative solution.
- [tex]\(x = -12\)[/tex]: This statement is also partially correct but incomplete for the same reason as the previous option.
So, the correct statement is:
[tex]\[
x \text{ can be 12 or -12}
\][/tex]
