Question

If x < 5 and y > 8, then find the value of |x - y|.

Answer 1

Given $x<5$ and $y>8$

Let $x<5$ ------ (1)

Consider $y>8$

$\Rightarrow -y<-8$ ------- (2)

adding (1) and (2)

$x+(-y)<\left(5\right)+(-8)$

$x-y<5-8$

$x-y<-3$

$(x-y)>|-3|$

$\Rightarrow |x-y|>3$