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Math Help - Review questions part 1 - equations involving the absolute value function.

  1. #1
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    Review questions part 1 - equations involving the absolute value function.

    Just started university, and I haven't really done math in like a half year at least. Because of this I am struggling a bit on some of the algebra/pre calc review, really would appreciate some help.

    Rewrite w/out abs. val. bars
    1. |2x - 1| if x < 1/2
    2. |2^x + 1|

    Solve for x.
    3. 1/x+a = 2/x-1 - 1/x-a, where a, b are constants
    4. x + (2 times sqrt x) - 3 = 0
    5. | (1 - 2x)/x | = 3x
    6. x^3 - 5x > or = 4x^2
    7. 2/x > or = 3
    8. - | 2x + 3 | < -4
    9. | 1 - 4x | - 7 < or = 2

    Thanks.
    Last edited by mr fantastic; August 28th 2011 at 12:40 PM. Reason: Re-titled.
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Some review I'm not sure on. PLEASE HELP.

    I don't think it's allowed to post so much exercices in one time. Start with one exercice, what have you tried? Where are you stuck?
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  3. #3
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    Re: Some review I'm not sure on. PLEASE HELP.

    Ok, for example 3.

    I realize I have to get the common denominator, but I don't know what to do from there.
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: Some review I'm not sure on. PLEASE HELP.

    Equation 3: (Where's b?)
    \frac{1}{x+a}=\frac{2}{x-1}-\frac{1}{x-a}
    1. You've a rational equation so first make sure the denominator will never be 0 by requiring:
     x\neq a, x\neq 1 and x\neq -a
    (For example at the end if you come to x=a then you're sure this cannot be the solution!)
    2. Put all the terms to one side and make a common denominator:
    \frac{1}{x+a}-\frac{2}{x-1}+\frac{1}{x-a}=0
    \Leftrightarrow \frac{(x-a)(x-1)}{(x+a)(x-a)(x-1)}-\frac{2(x+a)(x-a)}{(x-1)(x-a)(x+a)}+\frac{(x+a)(x-1)}{(x+a)(x-a)(x-1)}=0
    \Leftrightarrow \frac{(x-a)(x-1)-2(x+a)(x-a)+(x+a)(x-1)}{(x-a)(x+a)(x-1)}=0
    \Leftrightarrow (x-a)(x-1)-2(x+a)(x-a)+(x+a)(x-1)=0

    Take it from here.
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  5. #5
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    Re: Some review I'm not sure on. PLEASE HELP.

    Quote Originally Posted by xxStrikeback View Post
    Just started university, and I haven't really done math in like a half year at least. Because of this I am struggling a bit on some of the algebra/pre calc review, really would appreciate some help.

    Rewrite w/out abs. val. bars
    1. |2x - 1| if x < 1/2
    2. |2^x + 1|

    Solve for x.
    3. 1/x+a = 2/x-1 - 1/x-a, where a, b are constants
    4. x + (2 times sqrt x) - 3 = 0
    5. | (1 - 2x)/x | = 3x
    6. x^3 - 5x > or = 4x^2
    7. 2/x > or = 3
    8. - | 2x + 3 | < -4
    9. | 1 - 4x | - 7 < or = 2

    Thanks.
    #2 and #3 have been done for you.

    Please post some of the remaining questions according to the forum rules (MHF is not a service for answering questions en mass like this), many are similar so choose a few that represent your general difficulty. You will need to show some effort - what you have done and where you get stuck. It looks like you should also be getting help from your instructor or department tutor.

    Thread closed.
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