The correct option is [tex]\boxed{\bf option 2}[/tex].
Further explanation:
A compound inequality contains two or more inequalities such that they are separated by either “and” or “or”.
The Figure 1 (attached in the end) represents the compound inequality as [tex](-\infty,-4)[/tex] and [tex][3,\infty)[/tex].
Now [tex]-4[/tex] is excluded in the Figure 1 as the circle is hollow and [tex]3[/tex] is included in the Figure 1 as it is filled.
Option (1)
Here, the option (1) is [tex]x<-4[/tex] or [tex]x\geq 3[/tex].
This represents that the value of [tex]x[/tex] lies in the interval [tex](-\infty,-4)[/tex] as [tex]-4[/tex] is excluded in [tex]x<-4[/tex] or the value of [tex]x[/tex] lies in the interval [tex][3,\infty)[/tex] as [tex]3[/tex] is included in [tex]x\geq 3[/tex].
But either one of the possibility is true as the option contains “or”.
So, option (1) is incorrect.
Option (2)
Here, the option (2) is [tex]x<-4[/tex] and [tex]x\geq 3[/tex].
This represents that the value of [tex]x[/tex] lies in the interval [tex](-\infty,-4)[/tex] as [tex]-4[/tex] is excluded in [tex]x<-4[/tex] and the value of [tex]x[/tex] lies in the interval [tex][3,\infty)[/tex] as [tex]3[/tex] is included in [tex]x\geq 3[/tex].
Both the conditions of the given compound inequality is satisfied.
So, option (2) is correct.
Option (3)
Here, the option (3) is [tex]x\leq -4[/tex] or [tex]x<3[/tex].
This represents that the value of [tex]x[/tex] lies in the interval [tex](-\infty,-4][/tex] as [tex]-4[/tex] is included in [tex]x\leq -4[/tex] or the value of [tex]x[/tex] lies in the interval [tex](-\infty,3)[/tex] as [tex]3[/tex] is excluded in [tex]x<3[/tex].
But neither one of the possibility is true as compared to the given compound inequality.
So, option (3) is incorrect.
Option (4)
Here, the option (4) is [tex]x\geq -4[/tex] and [tex]x<3[/tex].
This represents that the value of [tex]x[/tex] lies in the interval [tex](-\infty,-4][/tex] as [tex]-4[/tex] is included in [tex]x\geq -4[/tex] and the value of [tex]x[/tex] lies in the interval [tex](-\infty,3)[/tex] as [tex]3[/tex] is excluded in [tex]x<3[/tex].
But neither one of the possibility is true as compared to the given compound inequality.
So, option (4) is incorrect.
Thus, the correct option is [tex]\boxed{\bf option 2}[/tex]
Learn more
1. Learn more about the whole numbers are positive integers https://brainly.com/question/1852063.
2. Learn more about the adding and simplifying the numbers https://brainly.com/question/894273
Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Number system
Keywords: Inequalities, compound inequality, interval, number line, real numbers, integers, whole numbers, open interval, closed intervals, semi closed intervals, semi-open intervals.
