So now let us look at a simple relationship that many students memorise instead of understand. Below, we see a absolute function graph.

Credits: Wikipedia
Credits: Wikipedia

Now we all know that |x|<a gives us -a<x<a. So how did that happen? Consider drawing a horizontal line, y=a in the graph above. |x| is less than a only when -a<x<a. Similarly, |x|>a is true only when x>a or x<-a. I do hope that the graphical representation helps here.

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