if-a-x-b-and-c-y-d-then-did-a-d-x-y-b-c-a-b-c-d-x-y-R-0-lt-c-0-lt-a-

Question Number 1335 by 123456 last updated on 23/Jul/15

if a ⩽ x ⩽ b and c ⩽ y ⩽ d then did

\frac{a}{d} ⩽ \frac{x}{y} ⩽ \frac{b}{c} ?

a, b, c, d, x, y \in R

0 < c

0 < a

Answered by prakash jain last updated on 23/Jul/15

a ⩽ x

a y ⩽ x y ∵ y > 0

a y ⩽ x d ∵ d ⩾ y

\frac{a}{d} ⩽ \frac{x}{y} ∵ d y > 0

x ⩽ b

x c ⩽ b c ∵ c > 0

x c ⩽ b y ∵ y ⩾ c

\frac{x}{y} ⩽ \frac{b}{c} ∵ y c > 0