# Thread: What am I doing wrong?

1. ## What am I doing wrong?

What am I doing wrong?

|2x+1|<|x+3| Solve for x.

So the correct answer is -4/3<x<2 based on my deductions. But my problem is my solution generates more answers.

+-(2x+1)<+-(x+3) =>

1) 2x+1<x+3 => x<2
2) 2x+1<-(x+3) => x<-4/3
3) -(2x+1)<(x+3) =>x>-4/3
4) -(2x+1)<-(x+3) => x>2

What am I doing wrong in the solution to get 2), 4) as wrong answers. I know I am probably having a brain fart and missing something obvious.

Thanks in advance for your help.

2. ## Re: What am I doing wrong?

Do not double post!

3. ## Re: What am I doing wrong?

For this problem, find the critical points of this equation and drop the signs for the particular ranges.

In this case, it's when 2x+1 = 0 and x+3 = 0, so x= -1/2 and -3

When x< -3, 2x+1 is negative and so is x+3
Hence on the condition that x< -3, -(2x+1) < -(x+3) if and only if 2x+1 > x+3 if and only if x>2

Does there exist solutions with x<-3 and x>2?

Repeat the same process for intervals (-3,-1/2), (-1/2, positive infinity). When solving the inequality the possible solution set intersected the interval in which the inequality is valid, will give you your solution

4. ## Re: What am I doing wrong?

First time post. Thought I posted in the wrong area.

5. ## Re: What am I doing wrong?

If that's the case, you just report your post and tell them what happened, the mods will move it for you.