To determine the minimum and maximum distances that Morgan's dog may be from the house, we can start by analyzing the given equation [tex]\( |x - 500| = 8 \)[/tex].
The absolute value equation [tex]\( |x - 500| = 8 \)[/tex] means we need to find the points [tex]\( x \)[/tex] on the number line that are 8 units away from 500. This gives us two scenarios:
1. The distance to one side of 500:
[tex]\[ x - 500 = 8 \][/tex]
2. The distance to the other side of 500:
[tex]\[ x - 500 = -8 \][/tex]
Now, let’s solve these two linear equations separately:
1. Solving [tex]\( x - 500 = 8 \)[/tex]:
[tex]\[ x = 500 + 8 \][/tex]
[tex]\[ x = 508 \][/tex]
2. Solving [tex]\( x - 500 = -8 \)[/tex]:
[tex]\[ x = 500 - 8 \][/tex]
[tex]\[ x = 492 \][/tex]
Therefore, the minimum distance from the house is 492 meters, and the maximum distance from the house is 508 meters.
Thus, the correct answer is:
[tex]\[ \boxed{492 \text{ meters and } 508 \text{ meters}} \][/tex]
