I have seen other answers explaining the topological proof up until the point of
$1/p + 1/q > 1/2$ and $p$, $q$ are greater than or equal to three
Then they proceed to say that the 5 platonic solids have the only values that satisfy these conditions. My question is how do I solve for these values? By 'graphing systems of linear inequalities with two variables'? I'm a high schooler so I see a system of inequalities and I try to graph it but the graph I get is weird... Below I show what I get when I just input "$1/p + 1/q > 1/2$": enter image description here Keep in mind that in that picture, I made '$p$' into '$x$', and '$q$' into '$y$'. Then I solved for y and put the inequality into Geogebra. This is because inputing '$1/x + 1/y > 1/2$' does not result in a graph for some reason, while '$y > (2x)/(x-2)$' does (even more confusion).
Am I totally wrong? How do you solve these inequalities and arrive to the desired numbers for the 5 platonic solids? Any help would be greatly appreciated! Please keep in mind that I'm a high schooler, though. I also haven't done any calculus yet. If the method is too advanced kindly just tell me the name, no need to explain. I'll remember it for when I'm older. Thank you.