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Math Help - need help inequality

  1. #1
    Junior Member
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    need help inequality

    please show me the plotting sets involved how you get them and explain the graph as draw visullly thanks for your help
    x+ 2y<=3
    2x-3y<=6
    solve the following system of lnear inequalities by graphing
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  2. #2
    Super Member

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    Hello, lizard4!

    Okay, here it is in baby-steps . . .


    Solve by graphing: . \begin{array}{ccc}x+ 2y & \leq & 3 \\2x-3y & \leq & 6 \end{array}

    Graph the first inequality . . .

    Graph the line: . x + 2y \:=\:3
    . . It has intercepts: (3,\,0),\;\left(0,\,\frac{3}{2}\right). .Draw the line.
    Solve the inequality for y\!:\;\;2y \:\leq \:-x + 3\quad\Rightarrow\quad y \:\leq\:-\frac{1}{2}x + \frac{3}{2}
    Since it is " \leq", shade the region below the line.
    Code:
                |
          *     |
          :::*  |
          ::::::o 3/2
          ::::::|::*
          ::::::|:::::*   3
        ---:-:-:+:-:-:-:-:o----------------
          ::::::|::::::::::::*
          ::::::|:::::::::::::::*
          ::::::|::::::::::::::::::*
          ::::::|:::::::::::::::::::::::*
                ||

    Graph the second inequality . . .

    Graph the line: . 2x - 3y \:=\:6
    . . It has intercepts: . (3\,0),\;(0,-2). .Draw the line.
    Solve the inequality for y\!:\;\;-3y \:\leq\:-2x + 6\quad\Rightarrow\quad y \:\geq \:\frac{2}{3}x - 2
    . . (When multiplying or dividing by a negative,
    . . . reverse the inequality . . . remember?]

    Since it is " \geq", shade the region above the line.
    Code:
                |
          ::::::|:::::::::::::::::::*
          ::::::|:::::::::::::::::*
          ::::::|:::::::::::::::*
          ::::::|:::::::::::::*
          ::::::|:::::::::::*
        ---:-:-:+:-:-:-:-:o----------------
          ::::::|:::::::* 3
          ::::::|:::::*
          ::::::|:::*
          ::::::|:*
          ::::::o -2
          ::::* |
          ::*   |
          *     |

    The solution is the region that has been shaded twice.
    Code:
                |
          *     |                   *
          :::*  |                 *
          ::::::o 3/2           *
          ::::::|::*          *
          ::::::|:::::*     *
        ---:-:-:+:-:-:-:-:o----------------
          ::::::|:::::::* 3  *
          ::::::|:::::*         *
          ::::::|:::*              *
          ::::::|:*                    *
          ::::::o -2
          ::::* |
          ::*   |
          *     |
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Soroban View Post
    Hello, lizard4!

    Okay, here it is in baby-steps . . .



    Graph the first inequality . . .

    Graph the line: . x + 2y \:=\:3
    . . It has intercepts: (3,\,0),\;\left(0,\,\frac{3}{2}\right). .Draw the line.
    Solve the inequality for y\!:\;\;2y \:\leq \:-x + 3\quad\Rightarrow\quad y \:\leq\:-\frac{1}{2}x + \frac{3}{2}
    Since it is " \leq", shade the region below the line.
    Code:
                |
          *     |
          :::*  |
          ::::::o 3/2
          ::::::|::*
          ::::::|:::::*   3
        ---:-:-:+:-:-:-:-:o----------------
          ::::::|::::::::::::*
          ::::::|:::::::::::::::*
          ::::::|::::::::::::::::::*
          ::::::|:::::::::::::::::::::::*
                ||

    Graph the second inequality . . .

    Graph the line: . 2x - 3y \:=\:6
    . . It has intercepts: . (3\,0),\;(0,-2). .Draw the line.
    Solve the inequality for y\!:\;\;-3y \:\leq\:-2x + 6\quad\Rightarrow\quad y \:\geq \:\frac{2}{3}x - 2
    . . (When multiplying or dividing by a negative,
    . . . reverse the inequality . . . remember?]

    Since it is " \geq", shade the region above the line.
    Code:
                |
          ::::::|:::::::::::::::::::*
          ::::::|:::::::::::::::::*
          ::::::|:::::::::::::::*
          ::::::|:::::::::::::*
          ::::::|:::::::::::*
        ---:-:-:+:-:-:-:-:o----------------
          ::::::|:::::::* 3
          ::::::|:::::*
          ::::::|:::*
          ::::::|:*
          ::::::o -2
          ::::* |
          ::*   |
          *     |

    The solution is the region that has been shaded twice.
    Code:
                |
          *     |                   *
          :::*  |                 *
          ::::::o 3/2           *
          ::::::|::*          *
          ::::::|:::::*     *
        ---:-:-:+:-:-:-:-:o----------------
          ::::::|:::::::* 3  *
          ::::::|:::::*         *
          ::::::|:::*              *
          ::::::|:*                    *
          ::::::o -2
          ::::* |
          ::*   |
          *     |
    How long did it take you to draw these?! You're really patient today to be drawing all these intricate diagrams like that
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  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
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    Well, there hasn't been too much traffic at my favorite math-help sites today.
    . . And this is what I do when I'm really bored.

    As to the Venn diagrams, I have a two-ring and a three-ring template
    . . already designed and stored in my archives.

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