SOLUTION: If a < b, then -a > -b. Why is this?

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Question 201188: If a < b, then -a > -b. Why is this?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Approach #1

a+%3C+b Start with the given inequality


cross%28a-a%29+%3C+b-a Subtract "a" from both sides.


0+%3C+b-a Combine like terms.


0-b+%3Ccross%28b-b%29+-a Subtract "b" from both sides.


-b%3C-a Combine like terms.


-a%3E-b Rearrange the inequality


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Approach #2


a+%3C+b Start with the given inequality


a%2F%28-1%29+%3E+b%2F%28-1%29 Divide both sides by -1. Note: dividing both sides of an inequality by a negative number will flip the inequality sign.


-a%3E+-b Reduce.



Here's an example: We can easily see that 5 < 10. If we change the signs we get -5 < -10 which is now NOT true. So we must change the sign to get -5 > -10 which is now true.