To determine which of the given numbers can replace the box [tex]\( \boxed{} \)[/tex] in the inequality [tex]\(-3 > \boxed{} > 0\)[/tex] to make a true statement, we need to evaluate each number and see if it satisfies the inequality.
Let's break it down step-by-step for each of the given numbers:
- 0
- 1
- 3
- 8
The inequality [tex]\(-3 > \boxed{} > 0\)[/tex] means the number must be greater than 0 and less than -3 at the same time.
1. Evaluate [tex]\(0\)[/tex]:
- Does [tex]\(0\)[/tex] satisfy both conditions [tex]\( -3 > 0 \)[/tex] and [tex]\( 0 > 0 \)[/tex]?
- [tex]\(0\)[/tex] does not satisfy [tex]\(0 > 0\)[/tex]
- Therefore, [tex]\(0\)[/tex] does not satisfy the inequality.
2. Evaluate [tex]\(1\)[/tex]:
- Does [tex]\(1\)[/tex] satisfy both conditions [tex]\( -3 > 1 \)[/tex] and [tex]\( 1 > 0 \)[/tex]?
- [tex]\(1\)[/tex] does not satisfy [tex]\(-3 > 1\)[/tex]
- Therefore, [tex]\(1\)[/tex] does not satisfy the inequality.
3. Evaluate [tex]\(3\)[/tex]:
- Does [tex]\(3\)[/tex] satisfy both conditions [tex]\( -3 > 3 \)[/tex] and [tex]\( 3 > 0 \)[/tex]?
- [tex]\(3\)[/tex] does not satisfy [tex]\(-3 > 3\)[/tex]
- Therefore, [tex]\(3\)[/tex] does not satisfy the inequality.
4. Evaluate [tex]\(8\)[/tex]:
- Does [tex]\(8\)[/tex] satisfy both conditions [tex]\( -3 > 8 \)[/tex] and [tex]\( 8 > 0 \)[/tex]?
- [tex]\(8\)[/tex] does not satisfy [tex]\(-3 > 8\)[/tex]
- Therefore, [tex]\(8\)[/tex] does not satisfy the inequality.
Given the conditions provided, none of the numbers 0, 1, 3, or 8 satisfy the inequality [tex]\(-3 > \boxed{} > 0\)[/tex].
Hence, the statement has no valid replacements from the provided choices. The resulting valid choices are:
[tex]\[ \boxed{[]} \][/tex]
