GIVEN:
a + b > 0
b – c < 0

Take bottom inequality and subtract b from both sides to get:
a + b > 0
–c < -b

Rewrite top inequality as follows:
0 < a + b
–c < -b

Since both inequality signs are facing the SAME direction, we can ADD the inequalities to get: -c < a
Now add c to both sides to get: 0 < a + c
Check the answer choices.... A is true


Okay, let's test the remaining answer choices...

B. c > a (must this be true??)
If a + b > 0 and b – c < 0, then it COULD be the case that a = 10, b = -2 and c = 7
In this case, it is NOT true that c > a
So, statement B need not be true


C. b > 0 (must this be true??)
Before we waste time testing a new set of questions, notice that we can RE-USE the values we used before.
That is, it COULD be the case that a = 10, b = -2 and c = 7
In this case, it is NOT true that b > 0
So, statement C need not be true

Answer: A