Question 193460: How do I solve the inequality x^3-x^2-6x>0?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! solve the inequality x^3-x^2-6x > 0
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Factor to find values that x cannot have:
x(x^2-x-6) > 0
x(x-3)(x+2) > 0
x cannot be 0, 3 or -2
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Draw a number line and plot x = -2, 0, and 3
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Test a value in each of the four resulting intervals to
see where solutions are for the inequality:
Test x = -5, you get (-5)^3-(-5)^2-6(-5) > 0 which is false
Test x = -1, you get (-1)^3-(-1)^2-8(-1) > 0 which is true
Test x = 1, you get 1 -1 - 6 > 0 which is false
Test x = 5, you get (5)^3 - (5)^2 -6(5) > 0 which is true
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Solutions are in -2 < x < 0 and 3 < x < +inf
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Cheers,
Stan H.
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