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    (Original post by Lunch_Box)
    Hi,

    I'm having trouble trying to put inequalities in context (Linear Programming chapter) and I am unsure how to approach them in a rational way.

    For instance:

    a) 4x ≦ y

    b) x ≧ 5y

    c) 'at most 5 times more x than y'

    d) 'at least 2 times less x than y'


    Thanks in advance.
    I never did D1 at A-level, but this is too simple to resist

    Hint:

    y > 5x

    means "5 times x [is] less than y"

    "at most" is associated with less than or equal to

    "at least" is associated with greater than or equal to.
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    (Original post by Indeterminate)
    I never did D1 at A-level, but this is too simple to resist

    Hint:

    y > 5x

    means "5 times x [is] less than y"

    "at most" is associated with less than or equal to

    "at least" is associated with greater than or equal to.


    Okay so for a) 4x ≦ y

    4 times x is less than y

    ... so at most y is 4 times more than x?
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    (Original post by Lunch_Box)


    Okay so for a) 4x ≦ y

    4 times x is less than y

    ... so at most y is 4 times more than x?
    No, you need "at least" in there

    4x \leq y \Rightarrow y \geq 4x
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    (Original post by Indeterminate)
    No, you need "at least" in there

    4x \leq y \implies y \geq 4x
    a) 4x ≦ y --> y ≧ 4x

    y is at least 4 times more than x

    b) x ≧ 5y

    x is at least 5 times more than y

    c) 'at most 5 times more x than y'

    x ≦ 5y

    d) 'at least 2 times less x than y'

    2x ≧ y
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    (Original post by Lunch_Box)
    a) 4x ≦ y --> y ≧ 4x

    y is at least 4 times more than x

    b) x ≧ 5y

    x is at least 5 times more than y

    c) 'at most 5 times more x than y'

    x ≦ 5y

    d) 'at least 2 times less x than y'

    2x ≧ y
    d) isn't quite right.

    Take y=6 or something. What values of x do you need?
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    (Original post by Indeterminate)
    d) isn't quite right.

    Take y=6 or something. What values of x do you need?
    Ooh the sign is the wrong way round.


    Thanks a lot.
 
 
 
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