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InequalityI'm having trouble with this inequality: 1/(x-5) < 4/5x I'm pretty sure the first step is to do this: 1/(x-5) - 4/5x < 0 But I'm stuck here. Could anyone nudge me in the right direction? |

Re: Inequality |

Re: InequalityThank you! |

Quote:
x + 20 > 0, 5x(x - 5) < 0 or x + 20 < 0, 5x(x - 5) > 0 For 5x(x - 5) < 0: 5x > 0, x - 5 < 0 or 5x < 0, x - 5 > 0 x > 0, x < -5 or x < 0, x > -5 For 5x(x - 5) > 0: 5x > 0, x - 5 > 0 or 5x < 0, x - 5 < 0 x > 0, x > -5 or x < 0, x < -5 For x + 20 > 0 and x + 20 < 0: x > -20 and x < -20, respectively x > -20, x > 0, x < -5 or x < 0, x > -5 OR x < -20, x > 0, x > -5 or x < 0, x < -5 x < 0, x > -5 is equivalent to -5 < x < 0 x > 0, x > -5 is equivalent to x > 0 x < 0, x < -5 is equivalent to x < -5 x > -20, x > 0, x < -5 or -5 < x < 0 OR x < -20, x > 0 or x < -5 x > -20 and -5 < x < 0 is equivalent to -5 < x < 0 x = 1 does not satisfy x > 0, x < -5 -5 < x < 0 OR x < -20, x > 0 or x < -5 x = 1 does not satisfy x < -20 and x > 0 x < -20 and x < -5 is equivalent to x < -20 ? -5 < x < 0 or x < -20 |

Re:Quote:
the whole equation by the square of the denominator giving u: then just draw it and determine negative domains |

Your solution is much easier. Thanks, daniel_an! |

Re: InequalityWow! Nice solution. |

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