Question 77747: Explain how you could solve the linear inequality
x^3 - x^2 - 6x >= 0
Hint: Factor the left hand side completely (you should have three factors) and use the same method for solving a quadratic inequality by making a table.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! x^3 - x^2 - 6x >= 0
Factor:
x(x^2-x-6)
=x(x-3)(x+2)
This has zeroes at x=-2, x=0, and x=3.
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Draw a number line and choose appropriate points for -2,0,and 3.
This creates 4 intervals.
Check each interval to see where the solutions lie.
You are looking for x(x-3)(x+2)>0
Int. (-inf,-2); check x=100; you get -*-*-<0 so no solutions there
Int. (-2,0); check x=-1; you get -*-*+ >0 so solutions here
Int. (0,3); check x=1 ; you get +*-*+ <0 so no solutions there
Int. (3,inf); check x=100; you get +*+*+>0 so solutions here
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Answer [-2,0] union [3,inf]
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Cheers,
Stan H.
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