Question

Given a > 0, b > 0, a > b and c ≠ 0. Which inequality is not always correct ?

(a) a + c > b + c

(b) a – c > b – c

(c) ac > bc

(d) \(\frac a{c^2}>\frac b{c^2}\)

Answer 1

Correct option is (c) ac > bc

It is given that both a and b are positive and a > b.

But it is not given whether c is positive or negative.

Now 

a > b

a ± c > b ± c

Also c² > 0 for any real value of c.

Hence

\(\frac a{c^2} > \frac b{c^2}\)

However,

ac > bc is only true if C > 0

If c < 0

ac < bc