Recall the following properties of the absolute value:
[tex]\begin{gathered} |a|\le b\Leftrightarrow-b\le a\le b, \\ |a|>b\Leftrightarrow a>b\text{ or a<-b.} \end{gathered}[/tex]
Therefore, all numbers between -3 and 3 can be represented by the following absolute value inequality:
[tex]|x|\le3.[/tex]
All numbers greater than 11 or less than -11 can be represented by the following absolute value inequality:
[tex]|x|>11.[/tex]
Answer:
1) All numbers between -3 and 3:
[tex]|x|\le3.[/tex]
2) All numbers greater than 11 or less than -11:
[tex]|x|>11.[/tex]
