Answers OC27 MATH COLL ALGEBRA-1200710-S1-Degele-VOL7006P Solving Absolute Value EquationsQuestion 1

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Solving Absolute Value Equations

Question 1 • (OC27) MATH COLL ALGEBRA-1200710-S1-Degele-VOL7006P

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?

Answer

A

496 meters and 500 meters

B

500 meters and 508 meters

C

492 meters and 508 meters

D

496 meters and 504 meters

Explanation

The leash lets the dog be as much as 8 meters closer to or farther from the house than Morgan is. Solving |x − 500| = 8 gives x = 500 − 8 = 492 or x = 500 + 8 = 508, so the minimum and maximum distances are 492 meters and 508 meters (choice C).

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