Algebra 2

Solve for x under the assumption that x > 0. Enter your answer in interval notation using grouping symbols.

x - (10/x) < 9

I need someone to show me how to work through this type of problem, I don't understand it.

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  1. x - 10/x < 9
    Since x>0, we can multiply by x and not change the direction of the inequality, so

    x^2 - 10 < 9x
    x^2 - 9x - 10 < 0
    (x-10)(x+1) < 0

    So, either
    (A): (x-10)<0 and (x+1)>0
    or
    (B): (x-10)>0 and (x+1)<0

    (A):
    x<10 and x > -1 or -1 < x < 10

    (B):
    x > 10 and x < -1
    can't happen

    So, -1 < x < 10
    But, we stipulated that x>0, so
    0 < x < 10
    x is in (0,10)

    Or, if you remember what parabolas look like, you can note that since the parabola opens upward, (x-10)(x+1) < 0 when x is between the roots. -1 < x < 10

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  2. x-3/x<-2

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