How to read the symbol $\gtreqqless$?

Question

The book I am currently reading, is written in a local language, uses the symbol $$\gtreqqless$$

Noted usage in the book (translated):

Let $f(x) = x^3e^{-3x}$ for x > 0. Then what is the maximum value of $f(x)$ ?

Solution : $\dotsc$ $f'(x) = 3e^{-3x}x^2(1-x)$... We have to work explicitly with $1 - x$ since $3e^{-3x}$ is positive for x > 0 $\therefore$ We have to see when 1 - x $\geqslant$ 0 and when 1 - x $\leqslant$ 0. We can see that 1 - x $\gtreqqless$ 0 $\Longleftrightarrow$ 1 $\gtreqqless$ x $\dotsc$

So how is the symbol read ,or, What does it mean ?

Edit: I have searched through the book and it does not provide any page on symbols used and no past explanation has been provided.

Answer 1

It is similar to $\pm$, so for example, $(a\pm b)^2=a^2\pm 2ab+b^2$, if you take a plus you take it everywhere, if you take a minus, you take it everywhere.

Likewise, if you consider $1-x>0$, you have $1>x$. (Here, we took the topmost symbol!)

If you have $1-x=0$, it means $1=x$; here we took the second symbol $=$. You can see the pattern now.

Hope this helps. Ask anything if not clear :)

Answer 2

It's a shorthand notation for $$ 1-x > 0 \iff 1 > x \quad\text{and}\quad 1-x = 0 \iff 1 = x \quad\text{and}\quad 1-x < 0 \iff 1 < x \, . $$