Given the intervals [tex]\((-\infty, -7]\)[/tex], [tex]\([-2, 3]\)[/tex], and [tex]\((-2, 5)\)[/tex], we can analyze them as follows:
1. Interval [tex]\((-\infty, -7]\)[/tex]:
- This interval includes all real numbers less than or equal to [tex]\(-7\)[/tex].
- In interval notation, it is expressed as [tex]\((-\infty, -7]\)[/tex].
2. Interval [tex]\([-2, 3]\)[/tex]:
- This interval includes all real numbers from [tex]\(-2\)[/tex] to [tex]\(3\)[/tex], inclusive of both endpoints.
- In interval notation, it is expressed as [tex]\([-2, 3]\)[/tex].
3. Interval [tex]\((-2, 5)\)[/tex]:
- This interval includes all real numbers greater than [tex]\(-2\)[/tex] and less than [tex]\(5\)[/tex], but does not include the endpoints [tex]\(-2\)[/tex] and [tex]\(5\)[/tex].
- In interval notation, it is expressed as [tex]\((-2, 5)\)[/tex].
These intervals can be written in their standard mathematical notation to reflect the sets they represent. Therefore, the intervals are:
- [tex]\((-\infty, -7]\)[/tex]
- [tex]\([-2, 3]\)[/tex]
- [tex]\((-2, 5)\)[/tex]
These representations help visualize the ranges of numbers included in each interval.
### Summary
The intervals provided are:
- [tex]\((-\infty, -7]\)[/tex]: This interval includes all numbers from negative infinity up to and including [tex]\(-7\)[/tex].
- [tex]\([-2, 3]\)[/tex]: This interval includes all numbers from [tex]\(-2\)[/tex] to [tex]\(3\)[/tex], including the endpoints.
- [tex]\((-2, 5)\)[/tex]: This interval includes all numbers between [tex]\(-2\)[/tex] and [tex]\(5\)[/tex], excluding the endpoints.
