Um, you don't. The sum of a positive and a negative integer can be positive:
[tex]8+(-3)=+5[/tex]
If what you're asking is, under what condition will the sum of a positive and negative be negative, then it's when the absolute value of the negative number is greater than the positive number. For example:
positive number: 8
negative number: -10
[tex]8+(-10)=-2[/tex]
This sum is negative. Note that [tex]\mid{-10}\mid\ \textgreater \ 8[/tex].
