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If: The signs are different.

 

This is because it can't remain constant. One will be addition, while the other subtraction, or they are both subtraction, but from different values.

 

Let's test it out. 
 

Positive: 

a = 2

b = 3

|2 - 3| = 1

|2| - |3| = 1

 

Negative:
a = -2

b = -3

|-2 + 3| = 1

|-2| - |-3| = 1

 

One positive, one negative:

a = 2

b = -3

|2 + 3| = 5

|2| - |-3| = -1

(same vice versa)

 

:)