Question 155334: solve the polynomial inequality and graph the solution set on a number lines. express the solution set in interval notation. 5x^2-3x is greater than or equal to 8.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! express the solution set in interval notation. 5x^2-3x is greater than or equal to 8
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5x^2-3x-8 >= 0
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1st: Solve the EQUALITY:
Factor to get:
5x^2-8x+5x-8 = =
x(5x-8) + (5x-8) = 0
(5x-8)(x+1) = 0
x = 8/5 or x = -1
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2nd:
Draw a number line and plot x = -1 and x=(8/5) on it.
Check a test-value in the INEQUALITY from each of the
three number number-line intervals.
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If x = -2 you get 5(-2)^2-(3*-2)-8 > 0; true so solutions in (-inf,-1)
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If x = 0 you get 5(0)^2 - 3*0 -8 >0 ; false so no solution in (-1,8/5)
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If x = 2 you get 5(2)^2 - 3*2 -8 > 0; true, so solutions in (8/5,+inf)
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Final answer: {x|-inf< x <-1} U {x|-1< x <+inf}
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Cheers,
Stan H.
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