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The equation provided is:

\[
|2x - 4| = 13
\]

To solve absolute value equations like this, we need to consider two cases:

### Case 1: 
The expression inside the absolute value is positive or zero, so we can remove the absolute value bars:

\[
2x - 4 = 13
\]

Solve for \(x\):
\[
2x = 13 + 4 \\
2x = 17 \\
x = \frac{17}{2} \\
x = 8.5
\]

### Case 2: 
The expression inside the absolute value is negative, so we remove the absolute value bars and negate the right-hand side:

\[
2x - 4 = -13
\]

Solve for \(x\):
\[
2x = -13 + 4 \\
2x = -9 \\
x = \frac{-9}{2} \\
x = -4.5
\]

### Final Answer:
The solutions are \(x = 8.5\) and \(x = -4.5\).

Would you like more details, or have any questions?

Here are some related questions for further practice:
1. Solve \( |3x + 2| = 10 \).
2. Solve \( |x - 5| = 8 \).
3. What happens if \( |2x - 4| = -5 \)?
4. Solve \( |4x + 1| = 7 \).
5. Solve \( |x| = 12 \).

**Tip:** When solving absolute value equations, always remember to create two cases: one where the expression inside the absolute value is positive, and one where it's negative.

Learn how to solve the absolute value equation |2x - 4| = 13 with detailed step-by-step instructions. This example covers core algebraic concepts including absolute value properties and solving linear equations. Suitable for students in Grades 8-10.

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