# Inequality problem

• Oct 3rd 2009, 07:44 AM
Kluringen
Inequality problem
Hi!
I need some help to get started With this problem.

For wich x is, $x+ \frac{\mid (x-1)\mid }{\mid x \mid}>1$

Next step i did was $x+\frac{\mid (x-1)\mid }{\mid x \mid}-1>0$

Now I have an equation on the left side $x+\frac{\mid (x-1)\mid }{\mid x \mid}-1=0$

So how do I proceed now to solve this equation with a pice of paper and a pencil ?
• Oct 3rd 2009, 08:08 AM
Quote:

Originally Posted by Kluringen
Hi!
I need some help to get started With this problem.

For wich x is, $x+ \frac{\mid (x-1)\mid }{\mid x \mid}>1$

Next step i did was $x+\frac{\mid (x-1)\mid }{\mid x \mid}-1>0$

Now I have an equation on the left side $x+\frac{\mid (x-1)\mid }{\mid x \mid}-1=0$

So how do I proceed now to solve this equation with a pice of paper and a pencil ?

HI
Obviously , x cant be 0

Since we know that |x| > 0

so its perfectly fine to do this :

|x-1|>|x|

(x-1)^2>x^2

x^2-2x+1-x^2>0

1-2x>0

I am sure you can continue here .
• Oct 3rd 2009, 12:03 PM
Krizalid
you dealt with the wrong inequality.

the problem is actually $x+\frac{|x-1|}{|x|}>1,$ but we can take your assumptions so this is $x|x|+|x-1|>|x|,$ so in order to solve this, we require so study three cases:

• $x<0.$
• $0
• $x>1.$