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# LHS Algebra 1 C5

### LHS Algebra 1 C5 Linear Inequalities

Term | Definition |
---|---|

Inequality | An open sentence that contains less than, greater than, less than or equal to, or greater than or equal to. |

set-builder notation | A more concise way of writing a solution set |

compound inequality | When two inequalities are considered together as a union or an intersection |

intersection | A compound inequality that contains "and" and only true if both inequalities are true. |

union | A compound inequality that contains "or" and is true if at least one of the inequalities is true. |

Addition property of Inequalities | If the same number is added to each side of a true inequality, the resulting inequality is also true. |

Subtraction property of Inequalities | If the same number is subtracted to each side of a true inequality, the resulting inequality is also true. |

Positive Multiplication property of Inequalities | If both sides of an inequality that is true are multiplied by a positive number, the resulting inequality is also true. |

Positive Division property of Inequalities | If both sides of a true inequality are divided by a positive number, the resulting inequality is also true. |

Negative Multiplication property of Inequalities | If both sides of an inequality that is true are multiplied by a negative number, the direction of the inequality sign is reversed to make the resulting inequality also true. |

Negative Division property of Inequalities | If both sides of a true inequality are divided by a negative number, the direction of the inequality sign is reversed to make the resulting inequality also true. |

boundary | |

half-plane | |

closed half-plane | |

open half-plane |