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

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

Start with the given inequality

Subtract "a" from both sides.

Combine like terms.

Subtract "b" from both sides.

Combine like terms.

Rearrange the inequality

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Approach #2

Start with the given inequality

Divide both sides by -1. Note: dividing both sides of an inequality by a negative number will flip the inequality sign.

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.
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