Question 334959
solve 4x^3 is greater than or equal to 16x
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4x^3 >= 16x
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4x^3-16x >= 0
4x(x^2-4)>= 0
4x(x-2)(x+2)>=0
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Solutions for the equality:
x = 0 or x = 2 or x = -2
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To find solutions for the inequality:
1. Draw a number line.
2. plot x = -2,0,2
3. test a check-point value in the inequality as follows:
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x(x-2)(x+2)> 0
Test x = -10 ; -*-*- > 0 ; false so no solutions in (-inf,-2)
Test x = -1 ; -*-*+ > 0 ; true so solutions in (-2,0)
Test x = +1 ; +*-*+ > 0 ; false so no solution in (0,2)
Test x = +10 ; +*+*+ > 0 ; true so solution in (2,+inf)
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Final solution for the original equation:
[-2,0]U[2,+inf)
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Cheers,
Stan H.