Question

The absolute value of the sum of two different integers with the same sign is 8. Pat says there are three pairs of integers that match this description. Do you agree? Explain

Answer 1

x, y - two different integers with the same sign.
The absolute value of the sum of the integers is 8.


`|x+y|=8 \\ \Downarrow \\ x+y=8 \hbox{ or } x+y=-8`

If the absolute value of the sum is 8, then the sum may be equal to 8 or -8.

There are 6 pairs of integers that satisfy this condition:
-7 and -1
-6 and -2
-5 and -3
1 and 7
2 and 6
3 and 5

Therefore, Pat is not right.