SOLUTION: Give reasons for the steps shown in each proof of each theorem. The domain of each variable is the set of real numbers unless otherwise stated. If 0 < a < b and 0 < c < d. 1

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Question 884312: Give reasons for the steps shown in each proof of each theorem. The domain of each variable is the set of real numbers unless otherwise stated.
If 0 < a < b and 0 < c < d.
1 a%3Cb and c%3E0
2. ac%3Cbc
3.c%3Cd and b%3E0
4.bc%3Cbd
5.ac%3Cbd

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1. a%3Cb Given, c%3E0 Given
2. ac%3Cbc Multiplication by a positive value (c%3E0) does not change the inequality (Multiplication rule of inequalities)
3. c%3Cd and b%3E0 Given
4. Same as 2, since d%3E0
5. From 4, bc%3Cbd and from 2, ac%3Cbc so then,
ac%3Cbc%3Cbd
So
ac%3Cbd