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

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Question 111754: If a < b, then -a > -b Why?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a%3Cb Start with the given inequality


cross%28a-a%29%3Cb-a Subtract "a" from both sides


0%3Cb-a Simplify


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


-b%3C-a Simplify


Now rearrange the inequality so the "a" term is first

-a%3E-b


To put it into English, if a is less than b, then the opposite of a is greater than the opposite of b. Let's say you had a=2 and b=5

So this is true

2%3C5

Now negate both sides.

-2%3C-5

Notice how -2 is not less than -5. So we must switch the signs to make it true

-2%3E-5

Since -2 is greater than -5, this is true. So it supports our claim. You can do this with any two numbers (provided that the second number is greater than the first) and it will work.