Question 284722: If a and b are negative and c is positive, which of the following must be true?
i) c - (a + b) > 0 ii) (a - c)(b - c) > 0 iii) (a - b)(c - b) > 0
a) (i) and (ii) only
b) (i) and (iii) only
c) (ii) and (iii) only
d) (i), (ii), and (iii)
e) none of these
Answer by CubeyThePenguin(3113)   (Show Source):
You can put this solution on YOUR website! i) c - (a + b) > 0
(positive) - (negative) > 0
This is always positive.
ii) (a - c)(b - c) > 0
ab - bc - ac + c^2 > 0
(positive) - (negative) - (negative) + (positive) > 0
This depends on the values of a, b, and c.
iii) (a - b)(c - b) > 0
ac - bc - ab + b^2 > 0
(negative) - (negative) - (positive) + (positive) > 0
This depends on a, b, and c.
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