Deviding and subtracting inequalities

Jinglander wrote:MGMAT says never do this. Can someone explain why

We can use counter examples to see why we can't divide, subtract or multiply inequalities.

- We know that 2<13 and 8<14, but when we subtract we get: (8-2)<(14-13), which simplifies to be 6<1 (no good

- Similarly, we know that 3<10 and 15<20, but when we divide we get: (15/3)<(20/10), which simplifies to be 5<2 (no good)

- Finally, we know that -3<-2 and 0<1, but when we multiply we get: (-3 x 0)<(-2 x 1), which simplifies to be 0<-2 (no good)

We can use logic to see why adding is okay. We'll use money as an example.

If Rod has more money than Bart (R>B), and Tod has more money than Lisa (T>L), then we also know that the combined wealth of Rod and Tod (R+T) will be greater than the combined wealth of Bart and Lisa (B+L).

In other word, if R>B and T>L then (R+T)>(B+L)

Jinglander wrote:Well you can multiply if everything is positive

Sure we can create some rules if we place certain restriction on the values.
However, if we place no restrictions, then addition is the only operation we can apply to combine inequalities.