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Math Help - Inequalities / Interval notation

  1. #1
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    Inequalities / Interval notation

    Find all values of x satisfying the inequalities. Present your answer using the interval notation and illustrate it with the help of the number axis.

    Hey guys.
    I just wanted to know if I'm on the right track with these questions.

    a) (x - 1) (2x + 3) > 0

    answer: x > 1 , x > - 1.5


    b) |7 + 2x| >/_ 3


    answer: x>/_ 3 (x is greater than or equal to 3)


    c) |2x - 7| </_ 3x - 10


    answer: x >/_ -2 or x >/_ -5 (x is greater than or equal to -2 or x is greater than or equal to -5)



    (Apologies for the greater than / equal to signs - I didn't know how to in put them. The underscore (_) represents the equal to sign)
    Last edited by jase03; April 27th 2012 at 04:00 AM.
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  2. #2
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    Re: Inequalities / Interval notation

    I'm just not sure about the interval notation and how you represent it on the number axis.
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  3. #3
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    Re: Inequalities / Interval notation

    type \leq for : \leq

    and

    type \geq for : \geq

    link
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  4. #4
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    Re: Inequalities / Interval notation

    Two comments about part a. If x>1 it will be greater than -3/2 so that part of the answer is just x>1

    Now use the fact that if both brackets are negative (that is <0) the product will be >0
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  5. #5
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    Re: Inequalities / Interval notation

    So its not x>-1.5 just x>1 ?
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  6. #6
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    Re: Inequalities / Interval notation

    Yes. Any value that is greater than 1 will also be greater than -1.5 so we don't need to write x greater than -1.5 as well as x greater than 1
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  7. #7
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    Re: Inequalities / Interval notation

    a) seems to be resolved

    b) |7 + 2x| \geq 3 for this one please remember the rule |x-a| \geq d => x-a \geq d or x-a \leq -d

    following the rule

    => |7+2x| \geq 3

    => 7+2x \geq 3 or 7+2x \leq -3

    => 2x \geq 3-7 or 2x \leq -3-7

    => x \geq -2 or x \leq -5 are your solutions

    c) similar situation but remember the rule |x-a| \leq d => -d \leq x-a \leq d
    Last edited by TheIntegrator; April 28th 2012 at 02:55 PM.
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