Let's analyze the comparisons step by step.
1. Comparison: [tex]\( -4 < -1 \)[/tex]
- To determine if [tex]\( -4 \)[/tex] is less than [tex]\( -1 \)[/tex], we consider their positions on the number line. The number [tex]\(-4\)[/tex] is located to the left of [tex]\(-1\)[/tex] on the number line. Therefore, [tex]\(-4\)[/tex] is indeed less than [tex]\(-1\)[/tex].
- Conclusion: [tex]\( -4 < -1 \)[/tex] is true.
2. Comparison: [tex]\( 2 < -4 \)[/tex]
- To determine if [tex]\( 2 \)[/tex] is less than [tex]\( -4 \)[/tex], we consider their positions on the number line. The number [tex]\(2\)[/tex] is located to the right of [tex]\(-4\)[/tex] on the number line. Therefore, [tex]\(2\)[/tex] is not less than [tex]\(-4\)[/tex].
- Conclusion: [tex]\( 2 < -4 \)[/tex] is false.
3. Comparison: [tex]\( -4 = 4 \)[/tex]
- To determine if [tex]\(-4\)[/tex] equals [tex]\(4\)[/tex], we note that they are distinct numbers, with [tex]\( -4\)[/tex] being negative and [tex]\(4\)[/tex] being positive.
- Conclusion: [tex]\( -4 = 4 \)[/tex] is false.
4. Comparison: [tex]\( -1 < 4 \)[/tex]
- To determine if [tex]\(-1\)[/tex] is less than [tex]\(4\)[/tex], we consider their positions on the number line. The number [tex]\( -1 \)[/tex] is located to the left of [tex]\( 4 \)[/tex] on the number line. Therefore, [tex]\(-1\)[/tex] is indeed less than [tex]\( 4 \)[/tex].
- Conclusion: [tex]\( -1 < 4 \)[/tex] is true.
Thus, the true statements among the given comparisons are:
- [tex]\( -4 < -1 \)[/tex]
- [tex]\( -1 < 4 \)[/tex]
Putting it all together, the true statements are:
- [tex]\( -4 < -1 \)[/tex]
- [tex]\( -1 < 4 \)[/tex]
Therefore, the correct selections are:
- [tex]\(\boxed{-4 < -1}\)[/tex]
- [tex]\(\boxed{-1 < 4}\)[/tex]
And the outcomes for the given comparisons are:
- [tex]\( -4 < -1 \)[/tex] is true.
- [tex]\( 2 < -4 \)[/tex] is false.
- [tex]\( -4 = 4 \)[/tex] is false.
- [tex]\( -1 < 4 \)[/tex] is true.
