Question

How do you solve `(3x +1)(5 - 10x) > 0`?

Answer 1

`(3x+1)(5-10x) = -30x^2+5x+5`

is an inverted parabola, cutting the `x` axis at the two points at which its value is zero, that is `x = -1/3` and `x = 1/2`

As `x -> -oo` or `x -> oo`, the `-30x^2` becomes dominant, and the quadratic has a negative value. So the region in which it has a positive value is `-1/3 < x < 1/2`