MHB Inequality with absolute value.

AI Thread Summary
The discussion revolves around solving the inequality 2x - |x+1| < 4. Participants share their approaches, emphasizing the importance of considering both cases for the absolute value. There is a focus on logical reasoning, specifically whether the solution requires both conditions to be true simultaneously or just one. A suggestion is made to broaden the answer by considering different ranges for x. The conversation highlights the collaborative effort to clarify the solution process.
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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