# 008A Sample Final A, Question 7

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**Question:** Solve

Foundations |
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1) How do we get to the first key step in solving any function involving absolute value equations? |

2) After this first key step how do we finish solving absolute value equations? |

Answer: |

1) We isolate the absolute value sign, so in this case we isolate . |

2) We create two equations based on whether the expression inside the absolute value is positive or negative. |

Then we solve both equations. |

Solution:

Step 1: |
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Isolate the absolute values. First by adding 7 to both sides, then dividing both sides by 2. |

This leads to |

Step 2: |
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Now we create two equations: and . |

Step 3: |
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Now we solve both equations. The first leads to the solution . The second leads to |

Final Solution: |
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