Answer :
Let's break down the inequalities to find which one matches the given conditions:
The student provided the inequalities:
- $6 < y[tex]: This means that[/tex]y[tex]is greater than $6[/tex].
- [tex]y \le 93[/tex]: This means that [tex]y[/tex] is less than or equal to $93$.
Together, these inequalities describe a range of values for [tex]y[/tex] such that [tex]y[/tex] is greater than $6[tex]and less than or equal to $93[/tex]. In other words, [tex]y[/tex] falls between $6[tex]and $93[/tex], but it includes $93[tex]and does not include $6[/tex].
Now we have to match this with one of the given double inequalities:
- $6 > y \ge 93[tex]- This expression says[/tex]y[tex]is less than $6[/tex] and at least $93[tex], which is not possible since[/tex]y[tex]cannot be less than $6[/tex] and simultaneously greater than or equal to $93$.
- $6 \le y < 93[tex]- This says[/tex]y[tex]is at least $6[/tex] and less than $93[tex]. This doesn't match because[/tex]y[tex]can be more than $6[/tex], not at least $6[tex], and[/tex]y[tex]can also equal $93[/tex].
- $6 < y \le 93[tex]- This means[/tex]y[tex]is greater than $6[/tex] and less than or equal to $93$, perfectly matching our original conditions.
- $6 \ge y > 93[tex]- This says[/tex]y[tex]is at most $6[/tex] and greater than $93[tex], which is not feasible as[/tex]y$ can't be both.
Therefore, the correct double inequality that represents the question is $6 < y \le 93$.
