Inequality problem

• Jun 2nd 2012, 06:32 AM
donnagirl
Inequality problem
If -1 < 2y < 0, what are the possible values of |y| - y ?

(|y| is the absolute value of y)

I know the interval is 0 < y < 1 but I don't how to show it algebraically..
• Jun 2nd 2012, 06:46 AM
Plato
Re: Inequality problem
Quote:

Originally Posted by donnagirl
If -1 < 2y < 0, what are the possible values of |y| - y ?
(|y| is the absolute value of y)
I know the interval is 0 < y < 1 but I don't how to show it algebraically..

If $-1<2y<0$ then $\begin{gathered} 0 < \left| y \right| < 0.5 \hfill \\ 0 < - y < 0.5 \hfill \\ \end{gathered}~~$ now add.
• Jun 2nd 2012, 06:51 AM
HallsofIvy
Re: Inequality problem
Quote:

Originally Posted by donnagirl
If -1 < 2y < 0, what are the possible values of |y| - y ?

(|y| is the absolute value of y)

I know the interval is 0 < y < 1 but I don't how to show it algebraically..

Unfortunately, what you "know" is wrong. If -1< 2y< 0 then, dividing by -2, 0< y< 1/2, not 1.
That's how Plato got his "0.5".
• Jun 2nd 2012, 03:04 PM
donnagirl
Re: Inequality problem
I thought the same too, but the solution of 0 < x < 1 came from collegeboard (it's a sample sat problem) How could they mislead us with the answer provided?
• Jun 2nd 2012, 03:21 PM
Plato
Re: Inequality problem
Quote:

Originally Posted by donnagirl
I thought the same too, but the solution of 0 < x < 1 came from collegeboard (it's a sample sat problem) How could they mislead us with the answer provided?

That solution is correct. Look at my reply. ADD and we get $0<|y|-y<1.$
• Jun 2nd 2012, 03:26 PM
donnagirl
Re: Inequality problem
How did you get those two intervals plato? Where did the -y come from as well? and why is the 0.5 on the right hand side? I get it to look like -0.5 < y < 0 when I worked out the algebra
• Jun 2nd 2012, 03:41 PM
Plato
Re: Inequality problem
Quote:

Originally Posted by donnagirl
How did you get those two intervals plato? Where did the -y come from as well? and why is the 0.5 on the right hand side? I get it to look like -0.5 < y < 0 when I worked out the algebra

You are given $-1<2y<0$.

Divide by two: $-0.5. Multiply by $-1:~~0<-y<0.5$.

If you know that $-3 then $1<|a|<3$. So from the given $0<|y|<0.5$.

Add those two together: $0<|y|-y<1~.$
• Jun 2nd 2012, 03:52 PM
donnagirl
Re: Inequality problem
thank you plato, I got it now!