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Math Help - Inequality

  1. #1
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    Inequality

    I have an inequality -4 < b < 2

    How I read it, -4 is equal to or less than b, and b is greater than 2

    or should it read; - 4 is equal to or less than b, and b is less than 2

    If this inequality was on a number line, where would "b" be represented?

    Thanks

    David
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  2. #2
    Super Member Quacky's Avatar
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    -4 is less than or equal to b, but b is less than 2.

    Think of the sign as a crocodile's mouth (it kind of looks like it) - it always eats the bigger number.

    So for 2 < 5 - it eats five because it's bigger.
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  3. #3
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    If it is written like that it means -4 <= b (which is the same as b >= -4) and b < 2. So your second version "- 4 is equal to or less than b, and b is less than 2" is correct.
    On a number line b would be somewhere between -4 and 2 or it could also be equal to -4.
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  4. #4
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    So I think I have the correct answer then?

    -4 < b < 2

    I am thinking that the solution is; 1 0, -1, -2, -3, -4

    How am I doing?

    Thanks

    David
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  5. #5
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    Assuming that you are only looking for integer solutions that would be correct.
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  6. #6
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    graph of -4 \le x < 2

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  7. #7
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    Looking at the graph and the typical answers I am given, it appears that I could still be wrong?

    If -4 < b < 2 then looking at the number line my answer could well be;

    -4 -3 -2 -1 0 1 2

    But the typical answers given are;

    -1 0 1
    -4 -3 -2 -1
    -5 -4 -3 -2 -1
    -5 -4 -3 -2 -1 0 1
    -1 0 1 2

    Kind of gets a bit confusing?
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  8. #8
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    Quote Originally Posted by David Green View Post
    Looking at the graph and the typical answers I am given, it appears that I could still be wrong?

    If -4 < b < 2 then looking at the number line my answer could well be;

    -4 -3 -2 -1 0 1 2

    But the typical answers given are;

    -1 0 1
    -4 -3 -2 -1
    -5 -4 -3 -2 -1
    -5 -4 -3 -2 -1 0 1
    -1 0 1 2

    Kind of gets a bit confusing?
    For an answer as a set of integers, note that 2 cannot be a solution as b < 2 does not include 2.

    What do you mean by "typical answers?"

    -Dan
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  9. #9
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    Quote Originally Posted by topsquark View Post
    For an answer as a set of integers, note that 2 cannot be a solution as b < 2 does not include 2.

    What do you mean by "typical answers?"

    -Dan
    Sorry just my writing, I should have said the listed answers?

    My understanding suggests the answer based on the list is;

    -4, -3, -2, -1

    anybody disagree?

    Thanks

    David
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  10. #10
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    What exactly is being asked for?
    If you are looking for all the given sets of numbers for which each of their elements satisfy the condition -4 =< b < 2,
    then I would say that the answer is both: {-1, 0, 1} and {-4, -3, -2, -1}.
    Last edited by VincentP; May 5th 2011 at 01:27 PM.
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  11. #11
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    Quote Originally Posted by VincentP View Post
    What exactly is being asked for?
    If you are looking for all the given sets of numbers for which each of their elements satisfy the condition -4 < b < 2,
    then I would say that the answer is both: {-1, 0, 1} and {-4, -3, -2, -1}.
    Thanks for your input into this problem, however what you advise about can't quite be right based on the answers we are given, which are;
    -1 0 1
    -4 -3 -2 -1
    -5 -4 -3 -2 -1
    -5 -4 -3 -2 -1 0 1
    -1 0 1 2

    Only one of the above can be the correct answer, I am not 100% sure, but based on the question -4 < b < 2, then looking at the list above of possible answers, only -4, -3, -2, -1 seems to fit the inequality, but as always I am open to any other explanations.

    Thanks

    David
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  12. #12
    Super Member Quacky's Avatar
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    Quote Originally Posted by David Green View Post
    Thanks for your input into this problem, however what you advise about can't quite be right based on the answers we are given, which are;
    -1 0 1
    -4 -3 -2 -1
    -5 -4 -3 -2 -1
    -5 -4 -3 -2 -1 0 1
    -1 0 1 2

    Only one of the above can be the correct answer, I am not 100% sure, but based on the question -4 < b < 2, then looking at the list above of possible answers, only -4, -3, -2, -1 seems to fit the inequality, but as always I am open to any other explanations.

    Thanks

    David
    There's always the possibility of a typo in the question. I think that perhaps it is supposed to be -5\leq b < 2

    As everyone here agrees that b ={-4, -3, -2, -1, 0, 1}, I think we can be fairly certain that the error lies not with us. Although, they said that to Galileo...
    Last edited by Quacky; May 5th 2011 at 09:09 AM.
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  13. #13
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    Quote Originally Posted by VincentP View Post
    Assuming that you are only looking for integer solutions that would be correct.
    I seem to have had my fair share of misunderstanding with this question, which after reading the quote above and re-reading the question again, I have now seen something different?

    Select the two lists of integer values of "b" in which the values satsify the inequality -4 < b < 2

    -1, 0, 1
    -4, -3, -2, -1
    -5, -4, -3, -2, -1
    -5, -4, -3, -2, -1, 0, 1
    -1, 0, 1, 2

    I think that the following are the correct answers;

    -4, -3, -2, -1

    -5, -4, -3, -2, -1, 0, 1

    Anybody disagree

    Thanks

    David
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  14. #14
    Super Member Quacky's Avatar
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    Quote Originally Posted by David Green View Post
    I seem to have had my fair share of misunderstanding with this question, which after reading the quote above and re-reading the question again, I have now seen something different?

    Select the two lists of integer values of "b" in which the values satsify the inequality -4 < b < 2

    -1, 0, 1
    -4, -3, -2, -1
    -5, -4, -3, -2, -1
    -5, -4, -3, -2, -1, 0, 1
    -1, 0, 1, 2

    I think that the following are the correct answers;

    -4, -3, -2, -1

    -5, -4, -3, -2, -1, 0, 1

    Anybody disagree

    Thanks

    David
    Yes, I disagree. -5 is not a possible solution.
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  15. #15
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    Just check the domain of "b" in the question.
    Apparently, it is asking for integer solutions,
    but maybe only negative integer solutions are being asked for
    (or maybe not).
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