Question 496151: Solve the inequality. Graph the solution set and write it in interval notation.
x(1-6x)<-2
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Solve the inequality. Graph the solution set and write it in interval notation.
x(1-6x)<-2
**
x(1-6x)≤-2
x-6x^2≤-2
x-6x^2+2≤0
multiply by (-1) and reverse inequality sign
6x^2-x-2≥0
(2x+1)(3x-2)≥0
number line:
<.....+.....-1/2]....-....[2/3....+......>
Interval notation:
(-∞,-1/2] U [2/3, ∞)
..
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.
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