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Math Help - Inequalities

  1. #1
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    Inequalities

    Solve the inequality. State the solution set using interval notation and graph.

    x-3/x+4>7

    x^2-5x-7<0
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  2. #2
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    Quote Originally Posted by pashah
    Solve the inequality. State the solution set using interval notation and graph.
    x-3/x+4>7
    x^2-5x-7<0
    Hello, pashah,

    I assume that your first problem reads: \frac{x-3}{x+4}>7

    Multiply by denominator. The next steps depends on the sign of the denominator!
    x-3>7x+28 \ \wedge\  x>-4
    -31>6x  \ \wedge\  x>-4
    -\frac{31}{6}>x \ \wedge\  x>-4. that means x\notin \mathbb{R}
    or
    x-3<7x+28 \ \wedge\  x<-4
    -31<6x  \ \wedge\  x<-4
    -\frac{31}{6}<x \ \wedge\  x<-4. So the solution is:
    -\frac{31}{6}<x <-4

    2nd problem:
    Solve this equation: x^2-5x-7=0. You'll get:
    x=\frac{5}{2}-\frac{\sqrt{53}}{2}\ \vee\ x=\frac{5}{2}+\frac{\sqrt{53}}{2}
    Because this equation belongs to a quadratic funtion which open upward, the part of the function between the zeros is below the x-axis, that means it is smaller than zero. Therefore your solution is:
    \frac{5}{2}-\frac{\sqrt{53}}{2}<x<\frac{5}{2}+\frac{\sqrt{53}}  {2}

    Greetings

    EB
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  3. #3
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    Quote Originally Posted by pashah
    Solve the inequality. State the ... graph....
    Hello, pashah,

    I've attached the graph of the 1rst problem.

    Greetings

    EB
    Attached Thumbnails Attached Thumbnails Inequalities-pashah_unglg.gif  
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  4. #4
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    Quote Originally Posted by pashah
    Solve the inequality. State the ...graph.
    x^2-5x-7<0
    Hello, pashah,

    I've attached the graph of your 2nd problem.

    Greetings

    EB
    Attached Thumbnails Attached Thumbnails Inequalities-pashah2_unglg.gif  
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