How to Solve Rational Inequalities?

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Homework Help Overview

The problem involves solving the rational inequality (x+2)/(x+1) - 2 < 0, which falls under the subject area of rational inequalities.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the steps taken to simplify the inequality and question the correctness of the least common denominator (LCD) identified. There is also confusion regarding the problem's title and whether it involves absolute value inequalities.

Discussion Status

Some participants have provided insights and clarifications regarding the nature of the problem, while others express uncertainty about the interpretations and calculations involved. There is no explicit consensus on the solution or approach yet.

Contextual Notes

Participants are grappling with the interpretation of the problem and the implications of the calculations, including potential misinterpretations of the problem statement.

priscilla98
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Homework Statement



Solve (x+2)/(x+1) -2 < 0

Homework Equations



LCD: x + 1

The Attempt at a Solution



(x+2-2x-2)/(x+1) < 0

(-x )/(x+1) < 0

But somehow, I got the wrong answer. The answer is (4, 7]. But I don't know where I went wrong.
 
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I tried everything I could to answer this problem. Am i right that the lcd is x + 1? Because when i multiply - 2 by x + 1, i end up having to cross out + 2 and -2.
 
I'm confused because you title this thread "Absolute Value Inequalities," but your problem does not have any absolute value symbols. Can you double check the problem, please? Is the problem this?
[tex]\frac{x+2}{x+1} -2 < 0[/tex]
Because that's what I'm interpreting.

Furthermore, according to WolframAlpha, the solution to what I typed above is
(-∞, -1) U (0, ∞), not (4, 7].69
 


Your right, its not absolute inequalities. It's rational equalities.

Okay, thanks a lot for answering this question. I really do appreciate it.
 

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