SOLUTION: Solve the inequality. Graph the solution set and write it in interval notation. x(1-6x)<-2

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.
RELATED QUESTIONS
20)Solve the inequality. Graph the solution set and write it in interval notation.... (answered by stanbon)

solve the inequality. Graph the solution set and write it in interval notation.... (answered by lwsshak3)

Solve the following inequality. Write the solution set in interval notation and graph it. (answered by MathLover1)

Solve the inequality, then write the solution set in interval notation, and graph. 6x... (answered by stanbon)

Solve each compound inequality. Write the solution set in interval notation and graph... (answered by stanbon)

Solve each inequality. Write the solution set in interval notation and graph it. 1.... (answered by MathLover1)

Solve the following inequality . Graph the solution set and write it in interval notation (answered by Edwin McCravy)

show how to solve the inequality ,graph the solution set and write it in interval... (answered by FrankM)

Solve the inequality. Then graph the solution set, and write it in interval notation.... (answered by robertb)