Question 63744
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Please help me solve this problem

Solve the inequality
3x^2-2x-1>- (greater than or equal) 0
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@praseenakos@yahoo.com's attempt at a "SOLUTION" is MOSTLY WRONG, as:
1) The quadratic {{{3x^2 - 2x - 1 >= 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 {{{- 1/6}}}, but {{{- 1/3}}}. instead
3) The positive solution, {{{x >= 1}}} is part of the other solution, {{{x >= - 1/3}}}. 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 = - 1/3}}} and x = 1 mean that there're 2 CRITICAL POINTS, {{{- 1/3}}} and 1.
The solutions will be the RANGES OUTSIDE these 2 critical points, including the critical points.
So, for {{{x = - 1/3}}}, the solution set will be the range to the LEFT of {{{- 1/3}}}, and {{{- 1/3}}}, itself, or: {{{x <= - 1/3}}}
And, for x = 1, the solution set will be the range to the RIGHT of 1, and 1, or {{{x >= 1}}}.</font></font></font></b></pre>