To determine the correct order of the given pair of numbers [tex]\(4\)[/tex] and [tex]\(-|-9|\)[/tex], we need to follow a few steps.
1. Evaluate the expression [tex]\(-|-9|\)[/tex]:
- First, find the absolute value of [tex]\(-9\)[/tex]. The absolute value of [tex]\(-9\)[/tex] is [tex]\(9\)[/tex]. This is because the absolute value function removes the negative sign and returns the non-negative magnitude of the number.
- Next, apply the negative sign outside the absolute value. So, [tex]\(-|9|\)[/tex] becomes [tex]\(-9\)[/tex].
2. Compare the two numbers:
- Now we have the numbers [tex]\(4\)[/tex] and [tex]\(-9\)[/tex] to compare.
- Clearly, [tex]\(4\)[/tex] is greater than [tex]\(-9\)[/tex], as any positive number is greater than any negative number.
Thus, the correct relationship between the numbers [tex]\(4\)[/tex] and [tex]\(-|-9|\)[/tex] is
[tex]\[ 4 > -|-9| \][/tex]
The correct answer is:
[tex]\[ > \][/tex]
