# Thread: Absolute value inequality question.

1. ## Absolute value inequality question.

Ok this is a really simple one I just can't remember the rules for this.
Say I have an inequality |x|<y from this we get -y<x<y right.
Now we have bee given that y>0.
Is it safe to assume that I can solve the given equation for x<y only?

I don't want to post the whole question as its a uni assignment its just this one little rule that is stopping me from having it solved. It has been 10 years since I learned this stuff at school so some things i need to check.

2. Originally Posted by rushton
Ok this is a really simple one I just can't remember the rules for this. Say I have an inequality |x|<y from this we get -y<x<y right.
Now we have bee given that y>0.
Is it safe to assume that I can solve the given equation for x<y only?
I don't fully understand the question.
So here is an example.
If $\displaystyle |x|<2$ then the solution is $\displaystyle -2<x<2$.
But you yourself said that above. What is your confusion?

3. Is it safe to assume that I can solve the given equation for x<y only?
Yes, it is safe since y is positive.

4. Its got 2 variables in it which is making it a little trickier.
Say we have -2y<x<2y.
If the question states that we are given y>0 does this mean that we only need to solve the equation for x<2y?
As -2y=2(-y) and as we are given y>0, -y<0 and thus we only calculate for the positive side.
I can answer the question in my assignment if this is so but if not it throws the answer off.
Also using random data inputs also kind of backs my suspicions that I can cancel out that negative side as the answers I get are always correct.

5. Originally Posted by Sambit
Yes, it is safe since y is positive.
Thanks thats what I thought I just really wanted to check.

6. If the question states that we are given y>0 does this mean that we only need to solve the equation for x<2y?
What equation do you mean? Are you talking about any equation that you have not posted? I think this is what you mean

7. Originally Posted by Sambit
What equation do you mean? Are you talking about any equation that you have not posted? I think this is what you mean
Yes basically, I was just trying to give a very generalised example to try and get the point across. Thanks very much for your help!

8. This thread is prefect example why posters should post the entire question. It should be as complete as possible.

9. I do agree to an extent but as it is concerning a university assignment I would not feel comfortable posting the whole question. If someone was to completely or partially answer the question I would have an unfair advantage and I hate the idea of being a cheat.