Do not double post!
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.
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.
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