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# Solving Absolute Value Equations

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Morgan is walking her dog on an 8-meter-long leash. She is currently 500 meters from her house, so the maximum and minimum distances that the dog may be from the house can be found using the equation |x – 500| = 8. What are the minimum and maximum distances that Morgan’s dog may be from the house?

A 496 meters and 500 meters

B 500 meters and 508 meters

C 492 meters and 508 meters

D 496 meters and 504 meters

Oct 23, 2018

### 1+0 Answers

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We have two  equations, here

x - 500  = 8           and                       - ( x - 500)  =  8

Add 500 to both sides                          Simplify

x  =  508                                              -x + 500  = 8

Add x to both sides. subtract 8 from both sides

492  = x

So   [ min. max ]   =   [ 492, 508 ]  ⇒  "C"

Oct 23, 2018
edited by CPhill  Oct 23, 2018