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To solve the absolute value equation \(|2x - 1| = 15\), we need to consider the two possible cases for the expression inside the absolute value:

### Case 1: Positive Case
\[ 2x - 1 = 15 \]

Solve for \(x\):
\[
2x = 15 + 1 \\
2x = 16 \\
x = \frac{16}{2} = 8
\]

### Case 2: Negative Case
\[ 2x - 1 = -15 \]

Solve for \(x\):
\[
2x = -15 + 1 \\
2x = -14 \\
x = \frac{-14}{2} = -7
\]

So, the solutions to the equation \(|2x - 1| = 15\) are \(x = 8\) and \(x = -7\).

### Answer
The correct choice is **A**. The solutions are \(x = 8, -7\).

Would you like further details or explanations? Here are some related questions:

1. How do you solve absolute value inequalities?
2. What are the different properties of absolute values?
3. How can absolute value equations have no solution?
4. What happens when the absolute value is set equal to a negative number?
5. Can you graph the solutions of this equation on a number line?

**Tip:** Always check the solutions by substituting them back into the original equation to ensure they satisfy the absolute value equation.

Solve the absolute value equation |2x - 1| = 15.

Learn how to solve the absolute value equation |2x - 1| = 15 with a detailed step-by-step solution. This problem covers key algebraic concepts, including solving absolute value equations and the properties of absolute values. Suitable for students in Grades 7-9.

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