Posted by WINSTON on Monday, March 10, 2014 at 11:20pm.
x(6x+1) < 15
6x^2 + x - 15 < 0
now you have a parabola. You need to find where it crosses the x-axis, and between those two points, it will lie below the x-axis.
(2x-3)(3x+5) < 0
so, the roots are at x = -5/3 and 3/2
Between those two values, the parabola lies below the x-axis.
As a check, let's try the original conditions.
x(6x+1) < 15
at x = -5/3, x(6x+1) = 15
at x = 3/2, x(6x+1) = 15
Now check something in between, say x = -1,0,1
f(x) = 5,0,7 all < 15.
How about a few outside -5/3 < x < 3/2 ?
f(-2) = 22 > 15
f(2) = 26 > 15
Take a look here:
http://www.wolframalpha.com/input/?i=x%286x%2B1%29+%3C+15
Initial Problem
x(6x + 1) < 15
Simplify left side.
6x^2 + x < 15
Move 15 to left side.
6x^2 + x - 15 < 0
Factor.
(2x - 3)(3x + 5) < 0
Now, x MUST be BETWEEN the LESSER value and the GREATER value. (it is between because this is a "LESS THAN" inequality)
-5/3 < x < 3/2