What is the solution for the absolute value equation \( | x - 3 | = 5 \)?

To solve the absolute value equation ( | x - 3 | = 5 ), we need to recognize what the absolute value represents. The expression ( | x - 3 | = 5 ) indicates that the distance between ( x ) and 3 on the number line is 5. This results in two possible equations that can be derived from the absolute value definition:

1. ( x - 3 = 5 )

2. ( x - 3 = -5 )

Starting with the first equation:

[ x - 3 = 5 ]

By adding 3 to both sides, we have:

[ x = 8 ]

Now, moving to the second equation:

[ x - 3 = -5 ]

Again, adding 3 to both sides results in:

[ x = -2 ]

Thus, the solutions to the absolute value equation ( | x - 3 | = 5 ) are ( x = 8 ) and ( x = -2 ). These solutions represent valid points that maintain the original condition imposed by the absolute value equation.

This makes the solution ( x = 8 ) or ( x = -2 ) the correct choice.