You can put this solution on YOUR website! One reason that comes to mind is for distances. Suppose you don't know if a is further away or b is further away. Then the distance between them might come out to be negative if you just do a-b or b-a, and that negative amount can mess things up. But no matter what, the absolute value of (a-b)= the absolute value of (b-a), which is the distance between them.
Another reason is because x^2 is always positive, so 2^2=4 and (-2)^2=4. But that means that if you know a^2=4 and you need to find what a is, you can't tell if it is 2 or -2, but you can tell that the absolute value of a is 2. If you have a more complicated problem, this thing (absolute value of a) that you know is 2 could be helpful.
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