SOLUTION: Please help me solve this qeuation : 3x²-11x+6 ≤ 0

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Question 1012117: Please help me solve this qeuation : 3x²-11x+6 ≤ 0
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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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