SOLUTION: Please help me solve this problem Solve the inequality 3x^2-2x-1>- (greater than or equal) 0

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Question 63744: Please help me solve this problem
Solve the inequality
3x^2-2x-1>- (greater than or equal) 0
Found 3 solutions by praseenakos@yahoo.com, rahman, MathTherapy:
Answer by praseenakos@yahoo.com(507) About Me  (Show Source):
You can put this solution on YOUR website!
QUESTION

3x^2-2x-1>- (greater than or equal) 0

ANSWER:
Here we can use quadratic formula to solve the problem.


If the quadratic equation is ax^2 + bx + c >-0,


then the solution is given by (please read the inequality as greater than or equal to)


x+%3E+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+





Now compare the given equation with the standard equation,
Then we have,
a=3
b= -2
c= -1

Now input all these values in the formula.
Then it comes like this,

x+%3E+%28-%28-2%29%2B-+sqrt%28+%28-2%29%5E2-4%2A3%2A%28-1%29+%29%29%2F%282%2A3%29+



x+%3E+%28%282%29%2B-+sqrt%28+4%2B12+%29%29%2F6+



x+%3E+%28%282%29%2B-+sqrt%28+16%29%29%2F6+


x+%3E+%28+2+%2B-+4+%29%2F6+

==> x> ( 2 + 4 ) / 6 or x > (2 - 4)/6
==> x > 6/6 or x > -2/6
==> x > 1 or x > -1/6


Which is the solutuion for your question.


Hope you understood.

Regards.

praseenakos@yahoo.co.in













Answer by rahman(247) About Me  (Show Source):
Answer by MathTherapy(10849) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me solve this problem

Solve the inequality
3x^2-2x-1>- (greater than or equal) 0
*************************************
@praseenakos@yahoo.com's attempt at a "SOLUTION" is MOSTLY WRONG, as:
1) The quadratic 3x%5E2+-+2x+-+1+%3E=+0 doesn't need to be solved using the quadratic formula, as it can be factorized
2) One of the solutions to the quadratic is NOT -+1%2F6, but -+1%2F3. instead
3) The positive solution, x+%3E=+1 is part of the other solution, x+%3E=+-+1%2F3. So, ordinarily, you CAN'T have both.
4) Solutions to INEQUALITIES are different from solutions to EQUATIONS. Inequalities' solutions need to
     be determined based on their CRITICAL POINTS' ranges.

     As such, IGNORE @praseenakos@yahoo.com's "SOLUTIONS," and ACCEPT the SOLUTION-SETS by Tutor @rahman(247)


The most concise explanation for the solutions?:
Solutions. x+=+-+1%2F3 and x = 1 mean that there're 2 CRITICAL POINTS, -+1%2F3 and 1.
The solutions will be the RANGES OUTSIDE these 2 critical points, including the critical points.
So, for x+=+-+1%2F3, the solution set will be the range to the LEFT of -+1%2F3, and -+1%2F3, itself, or: x+%3C=+-+1%2F3
And, for x = 1, the solution set will be the range to the RIGHT of 1, and 1, or x+%3E=+1.