Question

is the sum of two integers always greater than the difference between them.? why or why not.? give examples to support your answer

Answer 1

With negatives included, no.
You can add a negative with a positive and get a lesser number than you would when subtracting, only if you subtract the negative from the positive, making it become addition.
1 + (-1) = 0, while 1 - (-1) = 2. Some more examples are 3 and -8, 4 and -1.
Hope this helps! :)

Answer 2

No, inverse integers, are a simple example of the counter argument, and the greater the magnitude of those integers the greater the difference while the sum remains zero.  For example:

100 and -100

Their difference is 200 and their sum is zero