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: Recall absolute - value equation rules

The absolute - value equation \(|x - 500|=8\) can be split into two cases: \(x - 500 = 8\) and \(x - 500=-8\).

Step2: Solve the first case

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

Step3: Solve the second case

For \(x - 500=-8\), add 500 to both sides of the equation.
\(x=-8 + 500 = 492\).

Answer:

C. 492 meters and 508 meters