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# Absolute Value

### Module 9 : Absolute Value Equations and Inequalities

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

If A={x/x is an even number greater than 0 and less than 10} and B={3,4,5,6}, find A n B. | n=intersection List A={2,4,6,8} 4 and 6 are in both sets A and B therefore the answer is {4,6} |

If A={x/x is an even number greater than 0 and less than 10} and B={3,4,5,6} find A U B. | U=Union A={2,4,6,8} B={3,4,5,6} A U B={2,3,4,5,6,8} |

Solve 2<4-x<7 | 2 < 4-x < 7 2-4 < 4-x-4 <7-4 Subtract 4 from each side -2 > -x > 3 symbols will reverse because the numbers are now negative Divide all sides by -1 2 > x > -3 Solution = (-3,2) |

Solve IxI=4 | IxI = 4 IxI = 4 I4I = 4 I-4I = 4 4 = 4 True 4 = 4 True Solution {-4,4} |

Solve I2xI + 5 = 7 | I2xI + 5 = 7 I2xI = 2 Subtract 5 from both sides 2x = 2 or 2x = -2 Divide by 2 x = 1 or x = -1 {-1,1} |

Solve I2x+5I = -1 | No solution An absolute value of an expression is never negative |

Solve Ix-3I = I5-xI | x - 3 = 5 - x or x - 3 = - ( 5 - x ) 2x - 3 = 5 Add x x - 3 = - 5 + x Rewrite 2x = 8 Add 3 -3 = -5 False x = 4 Solution {4} |

Solve for x Ix-6I < 2 | -2 < x-6 < 2 -2 + 6 < x-6+6 < 2 + 6 Add 6 4 < x < 8 (4,8) solution |

Created by:
skommer