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# Absolute Value

What is a number's ABSOLUTE VALUE? | The absolute value of a number is it's distance from zero, (when plotted on a number line.) |

When solving an absolute value equation, first you must always | ISOLATE the absolute value. |

An absolute value expression must always be a non-negative number. | It can equal zero, or any positive. |

How do you ISOLATE an absolute value? | Move all other terms to the other side of the equal, or inequality sign. |

Absolute Value Equation Form |X| = a | |X| represents an expression containing a variable, (in this case equal to a.) Is a is a positive number, then |X| = a is equivalent to X = a and X = -a. If a = 0, then solve so that X = 0. |

Absolute Value Equation Form |X| = |Y| | |X| and |Y| are two separate expressions both containing a variable. X = Y and X = -Y |

Absolute Value Inequality Form |X| < a | In a Less Than Inequality you use a COMPOUND INEQUALITY to solve. -a < X < a When solving, all three terms must be treated equally. |

Absolute Value Inequality Form |X| > a | IN a GREATER THAN Inequality you set up TWO DISJOINT LINEAR INEQUALITIES to solve. X < -a or X > a |

What must you do to the inequality symbol(s) when multiplying or dividing both sides of an inequality by a NEGATIVE number? | REVERSE the inequality symbol. |

Absolute Value Inequality Form |x| < a or |x| > a | |x| represents a variable that is "a" distance from zero. |

Created by:
CoryBrydges