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Question

Suppose a<c and b<0. Which of the following must be true? ab < ac a+b<c+b a-b < c-b c/a > 1 Enter your answer as a list of those options that are always true. For instance, if you think only the first and third are true, enter 'A, C'.

Accepted Answer

If we consider a negative a and a positive c, we can see that this is not true. If we subtract b from both sides we get a<c which we know is true. Adding b to both sides again gives us a<c which we know is true. Again, if we consider a negative a and a positive c, we see that c/a is negative and hence not greater than 1. Thus, the answer is B, C.