To determine which statement correctly compares [tex]\(-9\)[/tex] and [tex]\(2\)[/tex], we need to examine each statement and reason if the comparison and explanation are correct.
### Step-by-Step Analysis:
1. Statement (a): [tex]\(-9 < 2\)[/tex] because [tex]\(-9\)[/tex] is to the left of [tex]\(2\)[/tex] on a number line.
- Comparison: [tex]\(-9 < 2\)[/tex]
- Examination: On a number line, [tex]\(-9\)[/tex] is indeed to the left of [tex]\(2\)[/tex]. As numbers increase from left to right, any number to the left of another number is smaller.
- Correctness: This statement is true because [tex]\(-9\)[/tex] is less than [tex]\(2\)[/tex].
2. Statement (b): [tex]\(9 > 2\)[/tex] because [tex]\(-9\)[/tex] is to the left of [tex]\(2\)[/tex] on a number line.
- Comparison: [tex]\(9 > 2\)[/tex]
- Examination: While it is true that [tex]\(9 > 2\)[/tex], the explanation connects [tex]\(-9\)[/tex] and [tex]\(2\)[/tex], which does not logically support the comparison of [tex]\(9\)[/tex] and [tex]\(2\)[/tex].
- Correctness: This statement is partially incorrect due to the explanation. The comparison [tex]\(9 > 2\)[/tex] is correct, but the reasoning is flawed.
3. Statement (c): [tex]\(-9 < 2\)[/tex] because [tex]\(-9\)[/tex] is to the right of [tex]\(2\)[/tex] on a number line.
- Comparison: [tex]\(-9 < 2\)[/tex]
- Examination: While the comparison [tex]\(-9 < 2\)[/tex] is true, the explanation provided is wrong. [tex]\(-9\)[/tex] is not to the right of [tex]\(2\)[/tex], it is actually to the left.
- Correctness: The statement's comparison is accurate, but the reasoning invalidates it, making the statement incorrect.
4. Statement (d): [tex]\(-9 > 2\)[/tex] because [tex]\(-9\)[/tex] is to the right of [tex]\(2\)[/tex] on a number line.
- Comparison: [tex]\(-9 > 2\)[/tex]
- Examination: This comparison is false since [tex]\(-9\)[/tex] is not greater than [tex]\(2\)[/tex]. Moreover, the given explanation is also incorrect because [tex]\(-9\)[/tex] is to the left of [tex]\(2\)[/tex] on a number line.
- Correctness: The entire statement is incorrect.
### Conclusion:
The only statement that is both logically and mathematically correct is:
- (a) [tex]\(-9 < 2\)[/tex] because [tex]\(-9\)[/tex] is to the left of [tex]\(2\)[/tex] on a number line.
Thus, the correct answer is:
(a) [tex]\(-9 < 2\)[/tex] because [tex]\(-9\)[/tex] is to the left of [tex]\(2\)[/tex] on a number line.
