Question 496151
Solve the inequality. Graph the solution set and write it in interval notation. 
x(1-6x)<-2
**
x(1-6x)&#8804;-2
x-6x^2&#8804;-2
x-6x^2+2&#8804;0
multiply by (-1) and reverse inequality sign
6x^2-x-2&#8805;0
(2x+1)(3x-2)&#8805;0
number line:
<.....+.....-1/2]....-....[2/3....+......>
Interval notation:
(-&#8734;,-1/2] U [2/3, &#8734;)
..
Explanation for signs in number line:
When x>2/3, the function>0
When going left thru the zeros, 2/3 and -1/2, the sign will switch if the zero is of an odd multiplicity, ie, 1,3,5, etc. The sign will not switch going thru a zero of even multiplicity like 2 or 4.
Zeros of given problem are of multiplicity 1, so the sign switches. Math teachers usually use charts to do this, but I have found this method to be a lot faster and simpler.