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# Module 9 - Math113

### Absolute Value Equations and Inequalities

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

What is |x| ? | This is the distance from 0. |

How many solutions are there for |x|=10 ? | There are two; x=10 and x=-10. |

What symbol denotes a union between to absolute value inequalities? | U |

What are you trying to find between two absolute value inequalities joined by the word, "and"? | The intersection. |

What is the first step to solving |x|+5>2 ? | Isolate the AV by subtracting 5 from both sides. This means |x|>-3 and there is no solution. |

If |x|< -2, how many solutions are there? | None; an AV inequality cannot equal a negative number. |

When "a" is positive, then |x|=a is equivalent to what? | x=-a, a |

What are the two forms of absolute value inequalities? | |x|>a and |x|<a |

How would you solve |x|>a ? | Create two separate inequalities: x>a and x<-a |

How would you solve |x|<a | Use the form -a<|x|<a. |

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