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Thread: Inequality Help: x+3/x-1 >= 0, (1-x)(x+2)/x(x+1) > 0

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    Inequality Help: x+3/x-1 >= 0, (1-x)(x+2)/x(x+1) > 0

    Hi,

    I'm currently in Precalculus and I'm just stumped on two problems and my book is not very helpful in going into detail on how to achieve a certain solution.

    Here is the problem: x+3/x-1 >= 0

    The book gives the solution of (-infinity,-3]U(1,infinity), how does the 1 get a "(" and not a "[". A step by step breakdown would be helpful, I'm just missing one piece to this puzzle and, again, the book isn't too helpful.

    The second inequality is (1-x)(x+2)/x(x+1) > 0

    The book gives the solution of (-2,-1)U(0,1), again it only gives the solution to the problem and no other examples. Kind of frustrating, but it's been a long time since I've had to mess with inequalities.

    Thanks for any help,

    Ryan

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    Quote Originally Posted by RC89 View Post
    Hi,

    I'm currently in Precalculus and I'm just stumped on two problems and my book is not very helpful in going into detail on how to achieve a certain solution.

    Here is the problem: x+3/x-1 >= 0

    The book gives the solution of (-infinity,-3]U(1,infinity), how does the 1 get a "(" and not a "[". A step by step breakdown would be helpful, I'm just missing one piece to this puzzle and, again, the book isn't too helpful.

    The second inequality is (1-x)(x+2)/x(x+1) > 0

    The book gives the solution of (-2,-1)U(0,1), again it only gives the solution to the problem and no other examples. Kind of frustrating, but it's been a long time since I've had to mess with inequalities.

    Thanks for any help,

    Ryan
    I believe your problem (function) is:

    (x+3)/(x-1) >= 0......................... This function is discontinuous at x = 1

    The takes on different meaning as you have posted → x + 3/x - 1 >= 0 ......................... This function is discontinuous at x = 0
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

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    Elite Member stapel's Avatar
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    Quote Originally Posted by RC89 View Post
    Here is the problem: x+3/x-1 >= 0
    What you've posted in an inequality (which is almost-certainly not formatted correctly; see previous response). "The problem" is the inequality, plus the instructions. Would it be correct to assume that the instructions were to "solve the inequality"? So the first exercise is as follows?

    . . . . .[tex]\mbox{Solve: }\, \dfrac{x\, +\, 3}{x\, -\, 1}\, \geq\, 0[/tex]

    Quote Originally Posted by RC89 View Post
    The book gives the solution of (-infinity,-3]U(1,infinity), how does the 1 get a "(" and not a "[".
    Who told you that "infinity" was a number, like "2", rather than a destination (something like "going onwards forever in that direction"), that "infinity" could be included in any interval?

    Quote Originally Posted by RC89 View Post
    The second inequality is (1-x)(x+2)/x(x+1) > 0

    The book gives the solution of (-2,-1)U(0,1), again it only gives the solution to the problem and no other examples.
    Your book provides no examples for solving rational inequalities? Ouch!

    Unfortunately, it is not reasonably feasible to attempt to provide here the days or weeks of instruction that you're needing. Instead, you'll need to attempt online self-study (or else hire a qualified local tutor) to learn the standard terms and techniques. For instance, here and here have explanations, followed by worked examples. Please study the lessons at both of these links (or at at least two other online lessons) before attempting the above-posted exercises. If you get stuck, you can then reply with a clear listing of your starting steps, continuing on to whatever point at which you got stuck.

    Thank you!

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    Quote Originally Posted by stapel View Post
    What you've posted in an inequality (which is almost-certainly not formatted correctly; see previous response). "The problem" is the inequality, plus the instructions. Would it be correct to assume that the instructions were to "solve the inequality"? So the first exercise is as follows?

    . . . . .[tex]\mbox{Solve: }\, \dfrac{x\, +\, 3}{x\, -\, 1}\, \geq\, 0[/tex]


    Who told you that "infinity" was a number, like "2", rather than a destination (something like "going onwards forever in that direction"), that "infinity" could be included in any interval?


    Your book provides no examples for solving rational inequalities? Ouch!

    Unfortunately, it is not reasonably feasible to attempt to provide here the days or weeks of instruction that you're needing. Instead, you'll need to attempt online self-study (or else hire a qualified local tutor) to learn the standard terms and techniques. For instance, here and here have explanations, followed by worked examples. Please study the lessons at both of these links (or at at least two other online lessons) before attempting the above-posted exercises. If you get stuck, you can then reply with a clear listing of your starting steps, continuing on to whatever point at which you got stuck.

    Thank you!
    Thanks for the links.

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    ^^^ FYI those were both examples in my book, I was simply asking for clarification. The chapter in my book is a review chapter and is 3 pages long, I didn't understand the rule that switches the inequality sign because the book doesn't go into detail. Thanks for the links, I'll be sure to not use this forum again.

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    Elite Member stapel's Avatar
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    Cool

    Quote Originally Posted by RC89 View Post
    'm just stumped on two problems and my book is not very helpful...it only gives the solution to the problem and no other examples.
    Quote Originally Posted by RC89 View Post
    FYI those were both examples in my book, I was simply asking for clarification.
    Oh... So when you said that these were "problems" (that is, exercises) and that your book gave no examples, this wasn't entirely accurate...? And, if you were "simply asking for clarification", then by what, precisely, were you confused? A clear listing of what the book gave you for these non-exercises would be very helpful, along with precise specifications of where you're getting lost.

    Thank you!

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    Quote Originally Posted by RC89 View Post
    … A step by step breakdown would be helpful …
    Quote Originally Posted by RC89 View Post
    … I'll be sure to not use this forum again.
    You may be at the wrong site because we don't provide step-by-step solutions, annotated or not.

    We're sorry that you wasted your time, here. You ought to have read the forum guidelines, before posting. (Twice, during the registration process, new members are instructed to read the guidelines.)
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

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