Find the solution set of the following inequality:
(x+1)/(x+5) ≥[1/(x+5)]-x

Please show complete solution and answer

Question

Find the solution set of the following inequality:
(x+1)/(x+5) ≥[1/(x+5)]-x

Please show complete solution and answer

anonymous · Answer

$$\dfrac{x+1}{x+5} \geq \dfrac{1}{x+5}-x$$
You already have a common denominator - if you multiply each term by that denominator, you can eliminate them.

elleblythe · Answer

@gypsy1274 I'd like to see a final answer please so I could check if my own answer is right

anonymous · Answer

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.

elleblythe · Answer

@gypsy1274  [-6, -5) U [0, +∞) ?

anonymous · Answer

I'm a bit rusty on the notation....Here is my answer:
$x\geq -6$

anonymous · Answer

$\left(\dfrac{x+1}{x+5} \geq \dfrac{1}{x+5}-x\right)\times (x+5)$
The denominators cancel with the first two terms leaving:
$x+1 \geq 1 - x^2-5x$

anonymous · Answer

Then I moved everything over to the left side and factored.

anonymous · Answer

Is that what you did?

anonymous · Answer

$$x \ge 0$$ $$-6 \le x < 5$$