Understanding this explanation about Big O notation
The best way to look at big $O$ notation is the following: $f(x)$ and $g(x)$ have the same $O$ complexity if you can find a positive constants $c_1, c_2 \in \mathbb{R}$ such that $f(x) \leq c_1 \cdot g(x)$ and $g(x) \leq c_2 \cdot f(x)$ for all $x$.

So, for example $4x$ and $10x$ are both in the same complexity class because $4x \leq 1 \cdot 10x$ and $10x \leq 3 \cdot 4x$. We name the complexity class they belong to $O(x)$, because $x$ is the simplest of all expressions of the form $c \cdot x$ so we use it as a representative.

Also, one can write equalities with big $O$;
$$O(4x) = O(10x) = O(x) = O(192839182x) \neq O(x^2) $$

Some basic complexity classes are (in order of complexity, from lower to higher):


$O(log n)$
$O(n)$
$O(n log n)$
$O(n^2)$
$\ldots$
$O(n^k)$
$\ldots$
$O(2^n)$
$\ldots$


and every complexity class on this list is not equal to any other.