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Thread: Inequality problem

  1. #1
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    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..
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  2. #2
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    Re: Inequality problem

    Quote Originally Posted by donnagirl View Post
    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.
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  3. #3
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    Re: Inequality problem

    Quote Originally Posted by donnagirl View Post
    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".
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  4. #4
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    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?
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  5. #5
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    Re: Inequality problem

    Quote Originally Posted by donnagirl View Post
    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 $\displaystyle 0<|y|-y<1.$
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  6. #6
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    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
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  7. #7
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    Re: Inequality problem

    Quote Originally Posted by donnagirl View Post
    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: $\displaystyle 0<|y|-y<1~.$
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  8. #8
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    Re: Inequality problem

    thank you plato, I got it now!
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