To find a statement that is equivalent to the given absolute value equation $|2x - 8| = 1$, we can rewrite the absolute value equation without the absolute value by setting up two separate equations based on the definition of absolute value:

Definition of Absolute Value:

$|A| = B \implies A = B \text{ or } A = -B$

Applying this Definition:

Given the equation $|2x - 8| = 1$, we can rewrite it as:

1. $2x - 8 = 1$
2. $2x - 8 = -1$

Solving Each Equation:

1. For $2x - 8 = 1$: $2x - 8 = 1$ Add 8 to both sides: $2x = 9$ Divide by 2: $x = \frac{9}{2}$

2. For $2x - 8 = -1$: $2x - 8 = -1$ Add 8 to both sides: $2x = 7$ Divide by 2: $x = \frac{7}{2}$

Equivalent Statement:

The equation $|2x - 8| = 1$ is equivalent to the statement: $2x - 8 = 1 \text{ or } 2x - 8 = -1$

Therefore, the correct choice is:

$2x - 8 = 1$ or $2x - 8 = -1$

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Would you like more details or have any questions?

Here are some related questions:

1. How do you solve other types of absolute value equations?
2. What are the steps to isolate the absolute value before solving?
3. How can absolute value inequalities be solved differently?
4. How does graphing absolute value functions help in understanding their equations?
5. What is the significance of absolute value in real-world problems?

Tip: Always check the validity of your solutions by substituting them back into the original absolute value equation to ensure they satisfy it!