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# Module 9 Math 113

### Inequalities and Absolute Values

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

solve x-7<2 and 2x+1<9 | x<9 and x<4 solution set is (-infinity symbol, 4) |

Solve 2<4-x<7 | (-3,2) |

Solve |5w+3|=7 | {-2,4/5} |

-2x<-10 and x-4<4 | 5<x<8 Interval notation (5,8) |

3<x-5<18 | (8,23) |

2(x-2)<4 or x+5>6 | All real numbers Interval notation (-infinity,infinity) |

|x|=4 | {-4,4} |

|2x-1|=5 | 3,-2 |

|x|+9=51 | -42,42 |

|7x|=0 | 0 |

Write an absolute value equation representing all numbers x whose distance from 0 is 25 units. | |x|=25 |

|7x-18|=|2x+5| | 13/9, 23/5 |

|z+3|=|z-5| | z=1 |

|x|=19 | -19,19 |

|x|=-8 | There is no solution. No number can have a negative absolute value. |

|6x|-6=24 | 5,-5 |

|x-4|+6=7 | 5,3 |

|6v-9|=-8 | No Solution |

|10+10c|-20=-2 | 4/5,-14/5 |

|2x-6|=|-16| | 11,-5 |

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