SOLUTION: Please help me solve the following: Solve the rational inequality. Express your answer using interval notation. (2x)/(x^2 + 16) ≤ 0 I think that I need to factor the

Algebra ->  Inequalities -> SOLUTION: Please help me solve the following: Solve the rational inequality. Express your answer using interval notation. (2x)/(x^2 + 16) ≤ 0 I think that I need to factor the      Log On


   

Question 1001185: Please help me solve the following:
Solve the rational inequality. Express your answer using interval notation.
(2x)/(x^2 + 16) ≤ 0
I think that I need to factor the bottom and make it: (2x)/(x+4)(x-4) but I'm not sure where to go from there. Please show work. Thank you!

Found 2 solutions by Edwin McCravy, stanbon:
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B16 cannot be factored as %28x%2B4%29%28x-4%29.
You are confusing x%5E2%2B16 with x%5E2-16 which can
be factored that way.

But Since 2 is positive and x%5E2%2B16 is always positive,
we can divide both sides by 2 and multiply both sides by
x%5E2%2B16 and get x%3C=0 which in interval notation
is  matrix%281%2C5%2C++++%22%28%22%2C-infinity%2C%22%2C%22%2C0%2C%22%5D%22%29

Edwin

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the rational inequality. Express your answer using interval notation.
(2x)/(x^2 + 16) ≤ 0
I think that I need to factor the bottom and make it: (2x)/(x+4)(x-4) but I'm not sure where to go from there. Please show work. Thank you!
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Note: Solve for the equality::
2x = 0
x = 0
That is part of the solution.
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Note: Solve the inequality::
2x and (x^2+16) MUST have opposite signs.
But x^2+16 is never negative.
So 2x MUST be negative
2x < 0 when x < 0
That is also part of the solution.
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Ans: x <= 0
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Cheers,
Stan H.
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