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

Now we all know that $|x| gives us $-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. 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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