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