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

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

• A. \(x = 5\) or \(x = 1\)
• B. \(x = 8\) or \(x = -2\)
• C. \(x = 3\) or \(x = 0\)
• D. \(x = 2\) or \(x = 4\)

Answer: (B)

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.

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.