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

1 Answer
George C.
May 25, 2015

#(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#

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