SOLUTION: How would you solve |x-3|-|x-7|=0

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Question 320342: How would you solve |x-3|-|x-7|=0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Break up the number line into 3 regions.
Region 1:(-infinity,3)
abs%28x-3%29=-x%2B3
abs%28x-7%29=-x%2B7
abs%28x-3%29-abs%28x-7%29=-x%2B3-%28-x%2B7%29
abs%28x-3%29-abs%28x-7%29=-x%2B3%2Bx-7
abs%28x-3%29-abs%28x-7%29=-4
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Region 2:(3,7)
abs%28x-3%29=x-3
abs%28x-7%29=-x%2B7
abs%28x-3%29-abs%28x-7%29=x-3-%28-x%2B7%29
abs%28x-3%29-abs%28x-7%29=x-3%2Bx-7
abs%28x-3%29-abs%28x-7%29=2x-10
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Region 3:(7,infinity)
abs%28x-3%29=x-3
abs%28x-7%29=x-7
abs%28x-3%29-abs%28x-7%29=x-3-%28x-7%29
abs%28x-3%29-abs%28x-7%29=x-3-x%2B7
abs%28x-3%29-abs%28x-7%29=4
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