Question 111754
{{{a<b}}} Start with the given inequality



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



{{{0<b-a}}} Simplify



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



{{{-b<-a}}} Simplify



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


{{{-a>-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<5}}}


Now negate both sides. 


{{{-2<-5}}}


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


{{{-2>-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.