This note is addressed to lilrhino
You asked about understanding the solution to inequalities not TeX.
As I wrote to you, it is all about the factors.
Consider . That factor is positive for and is negative for . For the factor is positive for and is negative for .
Now consider , that product is positive if both factors have the same ‘sign’; that product is negative if the factors have different ‘signs’.
This idea can be extended to any number of factors or quotients.
If you want to understand how inequalities work, then you need to understand the fundamental way factors contribute to the ‘signs’ of products and quotients.