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February 14, 2016
Posted by **WINSTON** on Monday, March 10, 2014 at 11:20pm.

can some one explain the problem and answer to me step by step please.. I missing the process

- math -
**Steve**, Monday, March 10, 2014 at 11:39pmx(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

- math -
**herp_derp**, Monday, March 10, 2014 at 11:42pmInitial 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