Prove that if 1 < x < 4 and 1 < y < 4, then |x – y| < 3

Given that 1 < x < 4 and 1 < y < 4

1<x<4……….eq(1)

1<y<4

Multiplying by (-) sign to the above inequality

As we know that the inequality sign changes when multiplied by (-) sign.

Therefore, -1>-y>-4………eq(2)

We can write eq(2) as -4<-y<-1

Now, adding eq(2) and eq(1)

We have, 1-4<x-y<4-1

Therefore, -3<x-y<3

So, by taking mod value of x-y we can write |x-y|<3.