Question

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 morgans dog may be from the house?
○ 496 meters and 500 meters
○ 500 meters and 508 meters
○ 492 meters and 508 meters
○ 496 meters and 504 meters

Explanation:

Step1: Solve the absolute value equation

The equation is \(|x - 500| = 8\). By the definition of absolute value, this means \(x - 500 = 8\) or \(x - 500 = -8\).

Step2: Find the maximum distance

For \(x - 500 = 8\), add 500 to both sides: \(x = 500 + 8 = 508\).

Step3: Find the minimum distance

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Answer:

Step1: Solve the absolute value equation

The equation is \(|x - 500| = 8\). By the definition of absolute value, this means \(x - 500 = 8\) or \(x - 500 = -8\).

Step2: Find the maximum distance

For \(x - 500 = 8\), add 500 to both sides: \(x = 500 + 8 = 508\).

Step3: Find the minimum distance

For \(x - 500 = -8\), add 500 to both sides: \(x = 500 - 8 = 492\)? Wait, no, wait. Wait, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? Wait, no, 500 - 8 is 492? 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