Inequality with absolute value.

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Discussion Overview

The discussion revolves around solving the inequality 2x - |x+1| < 4. Participants explore different approaches to the problem, including case analysis and logical reasoning regarding the conditions for the solution.

Discussion Character

  • Homework-related, Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant asks what methods have been tried to solve the inequality.
  • Another participant shares a link to their attempted solution, suggesting a case-based approach.
  • Several participants encourage the original poster, indicating they are close to a solution.
  • One participant proposes that the answer might be $x<5$.
  • Another participant raises a question about the logical conditions required for the solution, specifically whether both sides must be true simultaneously or if only one needs to be true.
  • A later reply suggests a broader interpretation of the solution, stating that for x<-1, the condition x<1 holds, and for x>-1, the condition x<5 holds.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the final solution to the inequality, and multiple interpretations of the conditions remain present.

Contextual Notes

There are unresolved aspects regarding the logical conditions necessary for the solution, as well as the implications of the case analysis presented.

vilhelm
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Solve 2x - |x+1| < 4.
 
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Re: Inequality with abs

What have you tried?
 
Re: Inequality with abs

I tried this

(you can pretty much ignore the table and go straight to case a and case b.

http://cl.ly/image/1Z1O0j1E2a0y
 
Re: Inequality with abs

So where are you stuck? You're almost there!
 
Re: Inequality with abs

You're virtually done now, time to smash the final obstacle :D
 
Re: Inequality with abs

Isn't $x<5$ the correct answer?
 
Re: Inequality with abs

You have to think logic here. Do both sides of your solution have to be true at the same time (logical AND), or does only one of them have to be true at a time (logical OR)?
 
Re: Inequality with abs

Would this be a better answer "for x<-1 we have x<1 and for x>-1 we have x<5" since it's a bit more broad?
 

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