Answer:
D. [tex]x<-6\mbox{ or } x>2[/tex]
Step-by-step explanation:
[tex]|x+2|-1>3[/tex]
First, add 1 to both sides:
[tex]|x+2|>4[/tex]
Now, you can split this into 2 equations. The value of the absolute value statement will be the same whether the statement inside is positive or negative. Example:
[tex]|2|=2\\|-2|=2[/tex]
Because of that, the [tex]x+2[/tex] could be positive or negative and still be true.
[tex]x+2>4\\-(x+2)>4[/tex]
Then, you can solve both of these inequalities. Top one here:
[tex]x+2>4\\x>2[/tex]
Bottom one:
[tex]-(x+2)>4[/tex]
Divide both sides by a -1 here, but be sure to invert the inequality sign:
[tex]x+2<-4\\x<-6[/tex]
The solutions are:
D. [tex]x<-6\mbox{ or } x>2[/tex]
