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Math Help - Set of values of X

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    Set of values of X

    Sketch the graph of y=\frac{(2(x+a))}{(x-1)}, where a>2. Hence find the set of values of x such that \frac{2(x+a)}{x-1}\leqslant |x+a|
    Last edited by Punch; May 7th 2011 at 10:43 PM.
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    Quote Originally Posted by Punch View Post
    Sketch the graph of y=\frac{(2(x+a))}{(x-1)}, where a>2. Hence find the set of values of x such that \frac{2(x+a)}{x-1}≤|x+a|
    And what did your graph tell you?

    -Dan
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    Quote Originally Posted by topsquark View Post
    And what did your graph tell you?

    -Dan
    From my understanding, the 2 graphs would intersect at 2 points, but i doubt this could help in anyway. Is there something I overlooked?
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Punch View Post
    From my understanding, the 2 graphs would intersect at 2 points, but i doubt this could help in anyway. Is there something I overlooked?
    Quote Originally Posted by Punch View Post
    Sketch the graph of y=\frac{(2(x+a))}{(x-1)}, where a>2. Hence find the set of values of x such that \frac{2(x+a)}{x-1}\leqslant |x+a|
    They intersect twice. Good. Now look at the inequality again. You are looking for all points on the 2(x + a)/(x - 1) curve that are lower on the graph (or equal to) the graph of |x + a|. So what parts of the function 2(x + a)/(x - 1) are below the lines?

    -Dan
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  5. #5
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    Quote Originally Posted by topsquark View Post
    They intersect twice. Good. Now look at the inequality again. You are looking for all points on the 2(x + a)/(x - 1) curve that are lower on the graph (or equal to) the graph of |x + a|. So what parts of the function 2(x + a)/(x - 1) are below the lines?

    -Dan
    but i cant find out since i cant draw the graph of |x+a| without knowing the value of a
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