AS level maths help

can somebody explain to me why you multiply by x^2 instead of just x for question 12c? Since the mark scheme for question 12a only requires you to find one x value, I'm wondering why it's different in this case.

you need to find an interval which is defined between 2 numbers. (think about it: as x is in the denominator, when it's negative 20/x will be negative, which can't be greater than 5, so x<4 would be incomplete) in any case it is a little misleading

you have to multiply by x^2. If you multiply by x it may be negative which would then make the > switch direction !

https://www.youtube.com/watch?v=xU4gEHuKL6c

recommend this video if you think you're still struggling understanding

If you're going to multiply through by something, then in this case you use x^2 because it's never negative. If you multiplied through by x; if x is positive, it's no problem, but if x is negative then the inequality sign would be reversed, but it's just x and you don't know if it's positive or negative - eek!