rational inequality with graphing

mrshan64

New member
Joined
Dec 16, 2005
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3
Hi-
This is the problem I have attempted several times to solve and graph.

x+3/x <= -2


This is one way I did it.

x+3/x -2 <= 0

x(x+3) -2 <= 0

x^2 + x <= 0

Now I am very lost.

Please help.
 
This Should Get You Started

Hi mrshan64:

I'm going to assume that your inequality is:

(x + 3)/x <= -2

The first goal is to get all of the terms on one side of the inequality symbol. To do this we add 2 to both sides.

(x + 3)/x + 2 <= 0

Combine the expression on the left side into a single fraction.

(x + 3)/x + (2x)/x <= 0

(x + 3 + 2x)/x = 0

(3x + 3)/x <= 0

Factor the numerater.

3(x + 1)/x <= 0

The values that make the expression on the left side zero or undefined are -1 and 0.

These two values divide the real number line into three segments.

Pick a test value in each segment and substitute it into the expression. The values that test true show which interval(s) make up the solution intervals.

Let us know if you need more help on this problem.

~ Mark :)
 
Thanks

Hi-

This does help me because it does make sense. On one version of my problem, I tried to add 2 but I just added it to one side. Now I see how this works. Thanks a bunch.

May I submit another problem as needed?
 
Re: Thanks

mrshan64 said:
May I submit another problem as needed?
Certainly, but please post new questions as new threads, not as replies to old threads (where they tend to be overlooked).

Thank you.

Eliz.
 
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