Question

We can divide or multiply an equality by an unknown without flipping inequality sign if and only if the unknown is greater than

Answer 1

We can divide or multiply an equality by an unknown without flipping inequality sign if and only if the unknown is greater than ​​$0$.

Example: $2<6$
On multiplying the inequality by unknown $x$, we get $2x<6x$ if and only if $x>0$

$\Rightarrow x=1$ is satisifying the inequality $(2x<6x)$
but $x=-1$ is not satisfying the inequality$(\because -2\text{is not less than}-6)$.

On dividing the inequality by unknown $x$, we get $\frac{2}{x}<\frac{6}{x}$ if and only if $x>0$

$\Rightarrow x=1$ is satisifying the inequality $(\frac{2}{x}<\frac{6}{x})$ but $x=-1$ is not satasfying the inequality$(\because -2\text{is not less than}-6)$