To find the opposite of [tex]\( |-4| \)[/tex], we need to follow these steps:
1. Determine the absolute value of [tex]\(-4\)[/tex]:
- The absolute value of a number is its distance from zero on the number line, without considering direction. Therefore, the absolute value of [tex]\(-4\)[/tex] is [tex]\(4\)[/tex].
2. Find the opposite of the absolute value:
- The opposite (or additive inverse) of a number is the number that, when added to the original number, results in zero. For the absolute value [tex]\(4\)[/tex], the opposite is [tex]\(-4\)[/tex].
So, by following these steps, we find that the opposite of [tex]\( |-4| \)[/tex] is [tex]\(-4\)[/tex].
Thus, the solution gives us:
- Absolute value of [tex]\(-4\)[/tex] is [tex]\(4\)[/tex].
- Opposite of this absolute value is [tex]\(-4\)[/tex].
In conclusion, the opposite of [tex]\( |-4| \)[/tex] is [tex]\(-4\)[/tex].
