SOLUTION: the difference of the aboslute value of two numbers is the same as the difference of the two numbers themselves. adding 1 to a numbers always increases its abosulte value. true or

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Question 917392: the difference of the aboslute value of two numbers is the same as the difference of the two numbers themselves. adding 1 to a numbers always increases its abosulte value. true or false, give a counterexample.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
definitions:
abs(x) means absolute value of x.
|x| means absolute value of x.
abs(x) means |x|

in order for the statement to be true, it has to be true under all conditions. if it's not true under all conditions, then it's false.

the difference of the absolute value of two number is not the same as the difference of the two numbers themselves.
this is false because sometimes it's true and sometimes it's false.
example where it's false.
5 - 5 = 0
abs(5) = 5
abs(5) - abs(5) = 5 - 5 = 0
it's false because the difference is the same (0 = 0).
example where it's true.
5 - (-5) = 5 + 5 = 10
abs(5) = 5
abs(-5) = 5
abs(5) - abs(-5) = 5 - 5 = 0
it's true because they're not the same (10 <> 0).

adding 1 to a number always increases its absolute value.
this is false because sometimes it's true and sometimes it's false.
example of where it's false.
abs(-5) = 5
abs(-5+1) = abs(4) = 4
it's false because 4 is not greater than 5.
example of where it's true.
abs(5) = 5
abs(5+1) = abs(6) = 6
it's true because 6 is greater than 5.