Starting with x−24/x<10 multiply everything by x.
x^2-24<10x
Subtract 10x from both sides.
x^2-10x-24 < 0
Factor.
(x-12)(x+2) < 0
(x+2) is always positive since x > 0, but (x-12) is negative when x is a value between 0 and 12. This negative value for (x-12) satisfies that the left side is less than 0. Thus the solution set for x is (0,12).
