Question

Solve the following absolute value inequality:

|3x - 1| - |x + 1| > 0

I don't understand how to do these forms of equations when there are two absolute value terms. Would anyone mind giving me a hand here?

Answer 1

\[|3x -1|>|x-1|\]

Answer 2

it's
3x+1>x+1
or
-(3x+1)<-(x+1)

Answer 3

isn't it? sorry haha i haven't done abs val inequalities in a while.. i might be wrong

Answer 4

I am not sure as to how you are guys are able to get rid of the absolute bars

Answer 5

Ishaan94, how do you know that?

Answer 6

Ok so you have to basically work the cases for when they are that many units away from the positive side, and that many units away from the negative side.

Answer 7

And since there are two absolute value arguments here, this means that you have 4 combos?

Answer 8

actually its
3x+1>x+1
x>0
and
3x+1<-(x+1)
4x<-2
x<-1/2

Answer 9

So what i said from before is that true? You have to go back to the equation and verify that LS > RS?

Answer 10

how can that b? x=5 works
(3*5-1)-(5-1)>0
15-1-4>0
10>0

Answer 11

x<0 or x>1

Answer 12

the main thing here, I believe, is that there are not 4 cases

Answer 13

wait a moment zarkon has that x<0 and x>1 so 1/2 shouldnt work
3(1/2)+1=5/2
1/2-1=-1/2
so 5/2-1/2>0
4/2>0
2>0
so zarkon is wrong as well

Answer 14

try that again

Answer 15

my bad messedd it up u r right

Answer 16

I am correct

Answer 17

if (3x-1)>0
then 3x>1 and x>1/3

then x+1>1/3+1>0

also

if x+1<0

then x<-1
then 3x-1<0

that kills two of the four cases

Answer 18

you can't have 3x-1>0 and x+1<0

you can't have x+1<0 and 3x-1>0

Answer 19

well zarkon is right sorry i did it all wrong ..it's kinda weird i did that way too wrong sorry : (

Answer 20

yes he is right 4 sure.