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Math Help - Absolute value equations and inequalities

  1. #1
    Junior Member
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    Absolute value equations and inequalities

    Help with these would be much appreciated. Thanks!

    Solve the equation graphically.
    |4x-3| = 5√(x+4)
    (4x-3) = 5√(x+4)
    4x= 5√(x+4) + 3
    x = (5√(x+4) + 3)/4??

    -4x+3=5√(x+4)
    x=(5√(x+4) -3)/-4

    Ok, assuming I did the math correctly (feel free to correct), I am not sure how to "Solve Graphically."

    Solve the inequality, express in interval notation.
    |x-8|>4
    x=12,
    -x=-4 so x=4?
    x=12,4 did I do this correctly??
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  2. #2
    MHF Contributor
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    Quote Originally Posted by Sxon View Post

    Solve the inequality, express in interval notation.
    |x-8|>4
    x=12,
    -x=-4 so x=4?
    x=12,4 did I do this correctly??

    |x-8|>4

    case 1 : x-8>4

    x>12

    case 2 : x-8<-4

     <br />
x<4<br />

    Thus the solution would be (12,\infty)U(-\infty,4)
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  3. #3
    MHF Contributor

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    Quote Originally Posted by Sxon View Post
    Help with these would be much appreciated. Thanks!

    Solve the equation graphically.
    |4x-3| = 5√(x+4)
    (4x-3) = 5√(x+4)
    4x= 5√(x+4) + 3
    x = (5√(x+4) + 3)/4??

    -4x+3=5√(x+4)
    x=(5√(x+4) -3)/-4

    Ok, assuming I did the math correctly (feel free to correct), I am not sure how to "Solve Graphically."
    To "solve graphically", graph! y= |4x-3| consists of two straight lines. As long as 4x-3>0 or x> 4/3, the graph is the line y= 4x- 3, a line with slope 4 and x-intercept (0, 4/3). As long as x< 4/3, the graph is the line y= -(4x-3)= 3- 4x, a line with slope -4 and x-intercept (0, 4/3).

    y= 5\sqrt{x+4} is part of y^2= 25(x+ 4) which is a parabola. Specifically, it is the part above the x-axis. You solve the equation by finding the x-coordinate of the point at which those intersect. Doing it on a graphing calculator makes it almost mindless.

    Solve the inequality, express in interval notation.
    |x-8|>4
    x=12,
    -x=-4 so x=4?
    x=12,4 did I do this correctly??
    math addict has already shown where you made your mistake on this: you are to solve the inequality not the equation. x= 12 and -4 (not 4)satisfy |x-8|= 4.
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