Inequality with absolute value.

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SUMMARY

The discussion centers on solving the inequality 2x - |x+1| < 4. Participants explore the logical conditions required for the solution, emphasizing the need to consider both cases of the absolute value. The correct approach involves analyzing the inequality in two scenarios: when x < -1 and x > -1. The final solutions derived from these cases are x < 1 and x < 5, respectively, leading to a comprehensive understanding of the inequality's constraints.

PREREQUISITES
  • Understanding of absolute value inequalities
  • Basic algebraic manipulation skills
  • Knowledge of logical operators (AND, OR)
  • Familiarity with solving linear inequalities
NEXT STEPS
  • Study the properties of absolute value functions
  • Learn to solve compound inequalities
  • Explore graphical representations of inequalities
  • Practice with similar absolute value inequality problems
USEFUL FOR

Students studying algebra, educators teaching inequality concepts, and anyone looking to strengthen their problem-solving skills in mathematics.

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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