Q:

Can someone explain this inequality transformation

I have seen this transformation but am not sure what laws are applied to achieve it.
$$
\frac{1}{2^{n+1}} \leq 10^{-6} \Rightarrow2^{n+1} \geq 10^6.
$$
I feel it is related to $x^{-1} = \frac{1}{x}$ and hence removing the negative exponents from both sides flips the inequality?

A:

Multiplying by $2^{n+1}>0$ and $10^6>0$ we get
$$10^6\le 2^{n+1}$$

