Question 201188
Approach #1


{{{a < b}}} Start with the given inequality



{{{cross(a-a) < b-a}}} Subtract "a" from both sides.



{{{0 < b-a}}} Combine like terms.



{{{0-b <cross(b-b) -a}}} Subtract "b" from both sides.



{{{-b<-a}}} Combine like terms.



{{{-a>-b}}} Rearrange the inequality



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Approach #2



{{{a < b}}} Start with the given inequality



{{{a/(-1) > b/(-1)}}} Divide both sides by -1. Note: dividing both sides of an inequality by a negative number will flip the inequality sign.



{{{-a> -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.