Answer:
Option (4) is correct.
[tex]x\leq 3[/tex] or [tex]x\geq -1[/tex] represent the given graph.
Step-by-step explanation:
Given : The graph representing the whole number line.
We have to choose the compound inequality that represent the given graph.
Since, the given graph shows a number line with all real numbers.
Consider each option one by one and we find the solution set for each.
1) [tex]-4\leq x\leq 4[/tex]
Since, the solution set contain only numbers between -4 and 4.
So it is false.
2) [tex]-2\leq x\leq -1[/tex]
This is a wrong representation.
So it is false.
3) [tex]x\leq -1[/tex] or [tex]x\geq 0[/tex]
This represents all real numbers excluding numbers between -1 and 0
So it is false.
4) [tex]x\leq 3[/tex] or [tex]x\geq -1[/tex]
So it represents all the real numbers on number lines as shown in graph below.
So, it is true.
[tex]x\leq 3[/tex] or [tex]x\geq -1[/tex] represent the given graph.
Option (4) is correct.
