Inequality problem

• Jun 2nd 2012, 05:32 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, 05:46 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 $\displaystyle -1<2y<0$ then $\displaystyle \begin{gathered} 0 < \left| y \right| < 0.5 \hfill \\ 0 < - y < 0.5 \hfill \\ \end{gathered}~~$ now add.
• Jun 2nd 2012, 05:51 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, 02:04 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, 02:21 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 $\displaystyle 0<|y|-y<1.$
• Jun 2nd 2012, 02:26 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, 02:41 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 $\displaystyle -1<2y<0$.

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

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

Add those two together: $\displaystyle 0<|y|-y<1~.$
• Jun 2nd 2012, 02:52 PM
donnagirl
Re: Inequality problem
thank you plato, I got it now!