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Simple equation question

  1. Mar 11, 2006 #1
    Hi Lets assume that my function is the following
    x(t)=2t+2 -1<=t<0

    Which of the following is correct?
    x(-t)=-2t+2 -1>=t>0 or
    x(-t)=-2t+2 -1>=-t>0 ]
    and why
     
  2. jcsd
  3. Mar 11, 2006 #2

    VietDao29

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    A small hint:
    If you let [tex]\alpha = -t[/tex], then [tex]x( \alpha ) = 2 \alpha - 1[/tex], right? Now what value should [tex]\alpha[/tex] take? Or in other words, what's the range for [tex]\alpha[/tex]? How about -t?
    Can you go from here? :)
    -----------------
    By the way, this should be posted in Precalculus Mathematics board.
     
  4. Mar 11, 2006 #3
    No i am not sure if i can make i :(
    I dont know when we have for example the -1<t<2 if i mytliply -1 what changes I should apply to the symbols < >
     
  5. Mar 11, 2006 #4

    VietDao29

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    Just change < to >, and vice versa, i.e > to <.
    For example, if 1 < t < 2, then -1 > t > -2.
    If -1 <= t <= 2, then 1 >= t >= -2.
    If you multiply both sides of an inequality by a negative number, then the signs will change. For example: t > 5 <=> -2t < -10.
    However, if you multiply both sides of an inequality by a positive number, the signs do not change.
    For example: x >= 2 <=> 10x >= 20.
    ----------
    Now, just answer my question, what's the range for [tex]\alpha[/tex]? And since [tex]\alpha = -t[/tex], what's the range for -t?
    Is the second statement correct? From there, is the first statement correct?
    Can you go from here? :)
     
  6. Mar 12, 2006 #5
    I just figured I'd post this little note from my lesson page since the thread creator seemed to be confused as to when to flip the inequality sign.:smile:

    [Copied and pasted here word for word:wink: ]

    If you must multiply or divide both sides of an inequality by a negative value, the inequality must reverse direction.
     
  7. Mar 12, 2006 #6
    "If -1 <= t <= 2, then 1 >= t >= -2.
    If you multiply both sides of an inequality by a negative number, then the signs will change. For example: t > 5 <=> -2t < -10."

    Thx a lot but why in first case whenu u multiply by -1 the t stays sanme?
    For me the correct is
    If -1 <= t <= 2, then 1 >=- t >= -2.

    Finally i agree with that
    For example: t > 5 <=> -2t < -10."
     
  8. Mar 12, 2006 #7

    VietDao29

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    Yeah, sorry, that's a typo. :blushing:
    So, can you solve the problem now? :)
     
  9. Mar 12, 2006 #8
    Of course thx a lot
     
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