Question

Given $a>0,b>0,a>bandc\ne 0.$ 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

The 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
$a>b$
$a\pm c>b\pm c$
Also $c^2>0$ 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 $c<0$
$ac<bc$
Hence answer is Option C.