Inequality with absolute value.

In summary, the conversation was focused on solving the inequality 2x - |x+1| < 4. The individual had already attempted to solve the inequality and was stuck on the final step. Through further discussion, it was determined that the correct solution was x < 5, with the clarification that it was a logical OR situation, where only one side of the solution had to be true at a time. The individual suggested a broader answer, stating that for x < -1, x < 1 and for x > -1, x < 5.
  • #1
vilhelm
37
0
Solve 2x - |x+1| < 4.
 
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  • #2
Re: Inequality with abs

What have you tried?
 
  • #3
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
 
  • #4
Re: Inequality with abs

So where are you stuck? You're almost there!
 
  • #5
Re: Inequality with abs

You're virtually done now, time to smash the final obstacle :D
 
  • #6
Re: Inequality with abs

Isn't $x<5$ the correct answer?
 
  • #7
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)?
 
  • #8
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?
 

FAQ: Inequality with absolute value.

What is "inequality with absolute value"?

Inequality with absolute value refers to mathematical inequalities that involve absolute value symbols. These symbols indicate the distance of a number from zero on a number line, and when used in inequalities, they can represent a range of numbers that satisfy the inequality.

How do you solve an inequality with absolute value?

To solve an inequality with absolute value, first isolate the absolute value expression on one side of the inequality. Then, rewrite the absolute value as a compound inequality with two separate inequalities, one for the positive value and one for the negative value. Solve each inequality separately to find the solution set.

Why is it important to understand inequality with absolute value?

Understanding inequality with absolute value is important because it allows us to accurately represent and solve real-world problems involving ranges of values. It also helps us to understand the concept of distance on a number line and how it relates to inequalities.

Can you graph an inequality with absolute value?

Yes, an inequality with absolute value can be graphed on a number line. The solution set will be represented by a shaded region on the number line, with the absolute value symbol indicating the distance from zero.

Are there any common mistakes when solving inequalities with absolute value?

Yes, common mistakes when solving inequalities with absolute value include not correctly isolating the absolute value expression, forgetting to write the compound inequality, and not considering both the positive and negative solutions. It's important to carefully follow the steps and check your work to avoid these mistakes.

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