008A Sample Final A, Question 7

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Question: Solve

Foundations:  
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:  
Isolate the absolute values. First by adding 7 to both sides, then dividing both sides by 2.
This leads to
Step 2:  
Now we create two equations: and .
Step 3:  
Now we solve both equations. The first leads to the solution . The second leads to
Final Answer:  

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