elleblythe
  • elleblythe
Find the solution set of the following inequality: (x+1)/(x+5) ≥[1/(x+5)]-x Please show complete solution and answer
Mathematics
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[\dfrac{x+1}{x+5} \geq \dfrac{1}{x+5}-x\] You already have a common denominator - if you multiply each term by that denominator, you can eliminate them.
elleblythe
  • elleblythe
@gypsy1274 I'd like to see a final answer please so I could check if my own answer is right
anonymous
  • anonymous
Sorry to be so suspicious, but so many on here are just looking for someone to do their homework for them. If you post your answer, I will post mine.

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elleblythe
  • elleblythe
@gypsy1274 [-6, -5) U [0, +∞) ?
anonymous
  • anonymous
I'm a bit rusty on the notation....Here is my answer: \(x\geq -6\)
anonymous
  • anonymous
\(\left(\dfrac{x+1}{x+5} \geq \dfrac{1}{x+5}-x\right)\times (x+5)\) The denominators cancel with the first two terms leaving: \(x+1 \geq 1 - x^2-5x\)
anonymous
  • anonymous
Then I moved everything over to the left side and factored.
anonymous
  • anonymous
Is that what you did?
anonymous
  • anonymous
\[x \ge 0\] \[-6 \le x < 5\]

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