Question 1012117
3x^2 - 11x + 6 <= 0


set the equation equal to 0 to get:


3x^2 - 11x + 6 = 0


factor to get (3x-2) * (x-3) = 0


set each of the factors equal to 0 and solve for x to get x = 2/3 and x = 3.


you have 2 checkpoints and 3 intervals to check.


first interval is x < 2/3.
second interval is x > 2/3 and < 3.
third interval is x > 3


just pick values in those intervals and determine whether they are positive or negative.


you will find that y is positive when x < 2/3 and y is negative when x < 2/3 and < 3 and y is positive when x > 3.


the original equation says that 3x^2 - 11x + 6 <= 0.


that occurs in the interval where x >= 2/3 and <= 3.


your solution is 2/3 <= x <= 3.


here's a graph of the equation.


you can see the interval where the equation is less than or equal to 0.


it is between x = 2/3 and x = 3, including x = 2/3 and x = 3.


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