Let's evaluate each statement related to subtracting integers:
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A positive integer minus a positive integer will always have a positive solution.
- This is false. For example, \(3 - 5 = -2\), which is negative.
-
A negative integer minus a positive integer will always have a positive solution.
- This is false. For example, \(-3 - 5 = -8\), which is negative.
-
A negative integer minus a negative integer will always have a negative solution.
- This is false. For example, \(-5 - (-3) = -5 + 3 = -2\), which is still negative, but \(-3 - (-5) = -3 + 5 = 2\), which is positive.
-
A positive integer minus a negative integer will always have a positive solution.
- This is true. For example, \(3 - (-2) = 3 + 2 = 5\), which is positive.
Based on the analysis, the last statement is the only one that is true:
A positive integer minus a negative integer will always have a positive solution.