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Math Help - liner inequalities

  1. #1
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    liner inequalities

    could some one show me the easiest way to graph liner inequalities like this
    Also what if the problem has two inequalities for one question

    problem 2x + 5y > -10
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by robpez View Post
    could some one show me the easiest way to graph liner inequalities like this
    Also what if the problem has two inequalities for one question

    problem 2x + 5y > -10
    First draw the boundary curve (or curves for multiple inequalities), in this
    case:

    2x + 5y = -10.

    Then shade the region on the side of the boundary curve for which the
    inequality holds, in this case the region above the line.

    (in the case of multiple inequalities the region over which they all hold
    is the intersection of the individual regions over which they individualy hold).

    RonL

    RonL
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  3. #3
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    robpez!

    Could some one show me the easiest way to graph linear inequalities like this:
    . . 2x + 5y > -10

    Also what if the problem has two inequalities for one question?

    As the Captain suggested, graph the equality (line).

    The line: .2x + 5y .= .-10 .has intercepts (-5,0) and (0,-2) **
    Graph this line . . . use a dotted line since it is not included in the solution.

    Solve the inequality for y (carefully!)
    . . 2x + 5y .> .-10
    . . . . . .5y .> .-2x - 10
    . . . . . . .y .> .(-2/5)x - 2

    Since the inequality is >, shade the region above the line.
    . . (If it was <, shade below the line.)

    The graph should look like this:
    Code:
          ::::::::::::::::|::::::::::::::::::
          ::::::::::::::::|::::::::::::::::::
          o:::::::::::::::|::::::::::::::::::
        - - - o:-:-:-:-:-:+:-:-:-:-:-:-:-:-:- -
             -5   o:::::::|::::::::::::::::
                      o:::|::::::::::::::
                        -2o::::::::::::
                          |   o::::::


    ** With the equation: .2x + 5y .= .-10, the intercepts are easily found.

    I perform what I call "Thumb Algebra".

    To find the x-intercept, let y = 0.
    . . Cover 5y with your thumb and solve: .2x = -10 . . x = -5

    To find the y-intercept, let x = 0.
    . . Cover 2x with your thumb and solve: .5y = -10 . . y = -2

    Got it?

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