Prove that if x < 3 and y > 7, then |x – y| > 4

Given that x < 3 and y > 7

We have, y>7

Multiplying by (-) sign to the above inequality

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

Therefore, -y<-7……..eq(1)

Also, x<3……..eq(2)

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

We have, x-y< -4……….eq(3)

Again multiplying by (-) sign to the above inequality

We have, -(x-y) > 4………eq(4)

By taking mod of x-y, we can say that |x – y| > 4.