1.04  Absolute Value Equations

Intermediate Algebra: One Step at a Time,  Page 42-46:   #9.

Dr. Robert J. Rapalje

Seminole State College of Florida

Sanford, FL  32773

To see Section 1.04, with explanations, examples, exercises, and answers, click here!

p.  46. 

9.      | 2 x – 3 | = | x + 6 |

           When solving an absolute value equal to another absolute value, remember that there are actually four possible equations to solve.  Fortunately, two of these four equations are the same as the other two, so you actually only need to solve two equations. 

 First Solution:      Positive = Positive

                                 2 x – 3  =  x + 6

                            2 x – x  =  6  + 3

                                    x   =  9

Second Solution:  Positive = Negative

                                 2 x – 3  =  – (x + 6)

                           2 x – 3  =  – x – 6

                           2 x + x  =  – 6  + 3

                                 3x   =  – 3

                                          x   =  – 1

Check solutions:          | 2 x – 3 | = | x + 6 |

            x   =  9            | 2 (9) – 3 | = | (9) + 6 |

                                | (18) – 3 | = | (9) + 6 |

                                         | 15 | = | 15 |

            x =  – 1   | 2 (– 1)    – 3 | = | (– 1) + 6 |

                                  |  (– 2)    – 3 | = | (– 1) + 6 |

                                              |  – 5  | = | 5  |

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