A+B+c=--100--A-B=15--B-c=8

We can simplify the given equation by first solving the absolute value expressions:

-|||-100-||| = -|-100| = -100

15-|||B+A||| = 15-|B+A|

Now we can substitute these values back into the original equation:

A+B+c - 100 = -100 A+B+c = 0

A+B - 15+|B+A| = 15-|B+A| We can split this into two cases:

1. B+A ≥ 0 In this case, the absolute value can be removed: A+B - 15+B+A = 15-B-A 2B = 30 B = 15 Substituting this into the first equation, we get: A + 15 + c = 0 A + c = -15

2. B+A < 0 In this case, the absolute value becomes negative: A+B - 15-B-A = 15+B+A -2A = 30 A = -15 Substituting this into the first equation, we get: -15 + B + c = 0 B + c = 15

Therefore, the solutions for A, B, and C are:

1. A = -15, B = 15, C = 0
2. A = -15, B = 0, C = 15 Note that these are the only solutions, as there are no other possible combinations of A, B, and C that satisfy the given equations.