Question 294664: Solve each inequality. 1/x is greater than or equal to 4x
Found 2 solutions by unlockmath, stanbon:
Answer by unlockmath(1688)   (Show Source):
You can put this solution on YOUR website! Hello,
Let's write this (1/x is greater than or equal to 4x) as:
1/x >= 4x Multiply by x on both sides to get:
1>=4x^2 Divide by 4 and then square root both sides to get:
+-1/2>=x
There we go.
Make sense?
RJ Check out a book at:
www.math-unlock.com
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! Solve each inequality.
1/x is greater than or equal to 4x
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1/x >= 4x
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4x - (1/x) <= 0
(4x^2-1)/x <= 0
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Solve the Equality:
(4x^2-1)/x = 0
Solve 4x^2-1 = 0
4x^2 = 1
x^2 = 1/4
x = 1/2 or x = -1/2
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Solve the Inequality:
Draw a number line and mark -1/2, 0, and 1/2 on it.
Test a value from each of the resulting intervals in the inequality:
(4x^2-1)/x < 0
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Test x = -1 to get +/- < 0; true so solutions in (-inf,-1/2)
Test x = -1/4 to get -/- >0, so no solutions in (-1/2,0)
Test x = +1/4 to get -/+ < 0, so solutions in (0,1/2)
Test x = 1 to get +/+ > 0, so no solutions in (1/2,+inf)
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Combining the solutions for the equality and the inequality you get:
(-inf,-1/2]U(0,1/2]
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Cheers,
Stan H.
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