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# Nonlinear Inequality

### Module 18: Nonlinear Inequalities in One Variable

Question | Answer |
---|---|

What are the four steps for Solving a Polynomial Inequality? | 1.Solve related equation. 2.Place solutions on a number line. 3.Test each region with a various testing point. 4.Write solution in interval notation. |

How would you solve this equation: 5x2 - 13x - 18 < 0 | First, factor the the equation using the FOIL method - (5x-18)(x+1) - and solve for x - x=18/5,-1. Then, solve for the three separate regions that form (ex. -2,1,4). Finally, write the answer in interval notation: (-1,18/5) |

What are the five steps for Solving Inequalities that contain Rational Expressions? | 1.Solve for values that make all denominators 0. 2.Solve related equation. 3.Separate number line into regions. 4.Choose a testing point for each region. 5.Write solution in interval notation. Do not include values that make any denominator 0. |

Just by looking at the equation x+9/x-2>_0, what number(s) automatically cannot be included in the answer? (Note: >_ : My lame greater than or equal to sign) | 2. The denominator cannot be 0 (which would be the difference of 2-2) so 2 is automatically not an answer. |

Just by looking at the equation x+9/x-2<0, what number(s) automatically cannot be included in the answer? | -9 and 2. The denominator cannot equal 0 which automatically eliminates 2. Also, because the equation cannot equal 0, -9 is eliminated. |

How would you solve this equation: x-2/x+5>_0 | Find the number that makes the denominator 0 (-5), then multiply the given denominator on both sides and solve for x (x=2). Test each region that formed from the equation(ex.-6,1,3). Finally, write the answer in interval notation: (-inf,-5)U[2,inf) |

Solve: 4x3 + 16x2 - 9x - 36 > 0 | Factor: 4x2(x+4)-9(x+4). Combine like terms:(4x2-9)(x+4). Factor: (2x+3)(2x-3)(x+4). Solve for x: x=3/2,-3/2,-4. Test and answer:(-4,-3/2)U(3/2,inf) |

Solve: x+7/x-3<0 | 0 Denominator: 3-3. Solve for x: -7. Test and answer: (-7,3). |

Solve: x4 - 9x2 + 20 <_ 0 | Factor. Use radicals if you have to. x= sqrt5,-sqrt5,-2,2. Test and solve. [-sqrt5,-2]U[2,sqrt5] |

Solve: x(x+6)/(x-6)(x+3)>_0 | 0 Denominators: 6-6,-3+3. Solve for x: 0,-6. Test and solve: (-inf,-6]U(-3,0]U(6,inf). |

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