Which number line shows the solution set for |d| > 3?

Answer:
Last option
[tex]d>3[/tex] or [tex]d<-3[/tex]
Step-by-step explanation:
The absolute value is a function that transforms any value x into a positive number.
Therefore, for the function [tex]f(x) = |x|[/tex] x> 0 for all real numbers.
Then the inequation:
[tex]|d|> 3[/tex] has two cases
[tex](d)[/tex] if [tex]d>0[/tex] (i)
[tex]-(d)[/tex] if [tex]d< 0[/tex] (ii)
We solve the case (i)
[tex]d> 3[/tex]
We solve the case (ii)
[tex]-d>3\\d < -3[/tex]
Then the solution is:
[tex]d>3[/tex] or [tex]d<-3[/tex]
Answer:
Last choice is the correct graph.
Step-by-step explanation:
We have been given inequality [tex]|d|>3[/tex]. Now we need to find out which of the given number lines shows the correct solution set for [tex]|d|>3[/tex].
We know that [tex]|x|>a[/tex] can be broken into :
[tex]x>+a[/tex] or [tex]x<-a[/tex]
Same way we can break [tex]|d|>3[/tex] into two parts as:
[tex]d>+3[/tex] or [tex]d<-3[/tex]
Since it has only < symbol but not equal so we make an open circle at both +3 and -3.
Hence last choice is the correct graph.