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# Compound Inequalitie

### Module 8

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

3x+1≤-11 and 3x≤0 | When you see the word and you know that you will be looking for the intersection. Simplifying these compound inequalities is the first step. x≤-4 and x≤0 Solution is (-∞,-4] |

x+7≥7 and x+5≤4 | Simplified x≥0 and x≤-1 This question has no solution |

-4x≤-12 or 3x-25≥-10 | Notice the compound inequality has the word OR in it. This means the answer will be the union of the solution sets. Also notice when dividing by a negative the inequality sign will flip. Simplified x≥3 or x≥5 Solution is [3,∞) |

x<-8 or x>-5 | Solution (-∞,-8) or (-5,∞) |

-12<3x-12≤7 | Simplify 0<x≤19/3 Solution (0,19/3] |

5x≤-25 and x≤0 | Notice that the the word and separates the two Simplified x≤-5 and x≤0 Solution (-∞,-5] |

The intersection of two sets, A and B, is the set of all elements common to both sets. A intersect B is denoted by A n B | Example: A=(x is an even number greater than 0 and less than 10) B=(3,4,5,6) The intersection of the sets is (4,6) |

The union of two sets, A and B, is the set of elements that belong to either of the sets. A union B is denoted by A U B | Example: A=(x is an even number greater than 0 and less tham 10) B=(3,4,5,6) The Union is (2,3,4,5,6,8) |

Are you looking for the Intersection or the union in this set 12x<-4 or 5x-17>-15 | Union, Notice that or seperates the two sets |

Are you looking for the Intersection or the union in this set x≤0 and x≥-2 | Intersection, Notice that the word and seperates the two sets |

Created by:
danieldombrowski