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Math Help - equations and inequallities

  1. #1
    Junior Member
    Joined
    Jul 2009
    Posts
    36

    equations and inequallities

    Hi

    I apologize If I didn't choose the right forum, for my new thread, but I really need some help with my homework

    / / Used for absolute value

    Solve Inequalities:

    a. /2x-3/<5
    b. /x^2-5x+6/>2
    c. /x/>x+1
    d. (x+1)(3x-5)<0
    e. 2/x/+3>5

    Solve equations:

    a. /x+1/-/x+2/=2
    b. /2x+3/=x^2

    I'd appreciate the way of solving too, not just the results

    Respectfully
    Alternative
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  2. #2
    MHF Contributor
    Joined
    Sep 2008
    From
    West Malaysia
    Posts
    1,261
    Quote Originally Posted by alternative View Post
    Hi

    I apologize If I didn't choose the right forum, for my new thread, but I really need some help with my homework

    / / Used for absolute value

    Solve Inequalities:

    a. /2x-3/<5
    b. /x^2-5x+6/>2
    c. /x/>x+1
    d. (x+1)(3x-5)<0
    e. 2/x/+3>5

    Solve equations:

    a. /x+1/-/x+2/=2
    b. /2x+3/=x^2

    I'd appreciate the way of solving too, not just the results

    Respectfully
    Alternative
    HI

    next time , do not post so many questions in one thread . Its against the rules of the forum . Post one or two , then try to solve the rest and come back if you are really lost .

    I will show you a few , then u try out the rest . OK ?

    (b) |x^2-5x+6|>2

    The properties of absolute value tells us that |x|>a , then x>a , x<-a

    so here x^2-5x+6>2\Rightarrow (x-1)(x-4)>0 .. try continue here

    then the other case would be x^2-5x+6<-2 .. this is complex so we can just ignore .

    (c) |x|>x+1

    square both sides .. x^2>x^2+2x+1

    2x+1<0

     <br />
x<-\frac{1}{2}<br />

    (a) |x+1|-|x+2|=2

    |x+1|=2+|x+2|

    square both sides x^2+2x+1=4+4|x+2|+x^2+4x+4

    -2x-7=4|x+2|

    Then square again ..

     <br />
4x^2+28x+49=16(x^2+4x+4)<br />
    carry on here .
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  3. #3
    Junior Member
    Joined
    Jul 2009
    Posts
    36
    Thank You Very Veryyyyy Much, And Sorry, I Didn't Meant To Break The Rules
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