If a and b are integers and a> b, then
| a | > | b | .

That would not be true

Because an integer can be negative lets set up an example

|-1|>|-2|

At first you might say -1>-2
But an absolute value takes its distance from 0
So it would be better to think about these numbers as positive

1>2

That's not true 

So 
|a|>|b| is not always true 

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