Correct notation for inequality equation

Question

I'm currently taking a Polynomial functions -course and learning about quadratic inequality equations.

Let's consider this equation:

$-x^{2}+7x<10$

The correct answer to this according to our book is simply

$x<2$ or $x>5$

But is there any other way to express this in a more mathematical way? I understand why this is expressed the way it is as we haven't learned about set theory yet, but I'd like to know how it is expressed "correctly".

Answer 1

Write it as $$x \in (-\infty,2)\cup(5,\infty)$$ or $$ x\in R - [2, 5]$$ or $$ x \in \{x: x < 2, x > 5, x\in R\}$$

See set notation for more details: http://www.mathsisfun.com/sets/set-builder-notation.html

Answer 2

You can write $\{x:x>5~~ \text{or} ~~~x<2\}$