To find the opposite of [tex]\( |-4| \)[/tex], follow these steps:
1. Determine the absolute value:
- The absolute value of a number is its distance from zero on the number line, regardless of direction. This is always a non-negative number.
- For the given number, [tex]\(-4\)[/tex]:
[tex]\[
|-4| = 4
\][/tex]
2. Find the opposite:
- The opposite of a number [tex]\( a \)[/tex] is defined as [tex]\(-a\)[/tex].
- So, the opposite of [tex]\( 4 \)[/tex] is:
[tex]\[
-4
\][/tex]
Thus, the absolute value of [tex]\(-4\)[/tex] is [tex]\( 4 \)[/tex], and its opposite is [tex]\(-4\)[/tex].
Hence, the opposite of [tex]\( |-4| \)[/tex] is [tex]\(-4\)[/tex].
Therefore, the final result is:
[tex]\[ (4, -4) \][/tex]
