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# Absolute Value

### Absolute Value Equations & Inequalities

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

TRUE OR FALSE: An absolute value equation can equal 0. | FALSE |

|x| = A is equivalent to: | X = A OR X = -A |

|x| < A is equivalent to: | -A < X < A |

|x| > A is equivalent to: | X < -A OR X > A |

SOLVE: |x + 4| = -8 | NO SOLUTION Absolute value's are always positive, and can not equal anything negative. |

SOLVE: |x + 8| < -4 | NO SOLUTION Absolute value's are always positive, and can never be less than a negative number. |

SOLVE: |x| > -6 | (-infinity,infinity) No matter what x's value is, it will always be positive, which is greater than a negative. |

SOLVE: |x| > 4 | (-infinity,-4)U(4,infinity) Any number (negative or positive) greater than 4 is a solution. Parenthesis are used to denote the solution is NOT EQUAL TO. |

SOLVE: |x| < 5 | -5 < x < 5 |

SOLVE: |x + 2| > 6 | x + 2 > 6 OR x + 2 < -6 x > 4 OR x < -8 (-infinity,-8)U(4,infinity) |

Created by:
along500