To solve the equation \( |2x - 4| = 10 \), we need to break it into two cases, as the absolute value can result in either a positive or negative expression.

### Case 1: \( 2x - 4 = 10 \)
\[
2x - 4 = 10
\]
Add 4 to both sides:
\[
2x = 14
\]
Now divide by 2:
\[
x = 7
\]

### Case 2: \( 2x - 4 = -10 \)
\[
2x - 4 = -10
\]
Add 4 to both sides:
\[
2x = -6
\]
Now divide by 2:
\[
x = -3
\]

### Final Answer:
The solutions are \( x = 7 \) and \( x = -3 \).

Would you like further clarification on absolute value equations or more details on this solution?

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Here are 5 related questions:
1. How do you solve absolute value inequalities?
2. What is the graphical interpretation of absolute value equations?
3. How do you solve the equation \( |3x + 5| = 8 \)?
4. What happens if the equation \( |2x - 4| = -10 \) is given instead?
5. Can you solve absolute value equations using a different method, like squaring?

**Tip:** When solving absolute value equations, always remember to consider both the positive and negative cases!

Learn how to solve the absolute value equation |2x - 4| = 10 with a step-by-step solution. This problem involves key algebraic concepts, including absolute value properties, and is suitable for students in Grades 6-8.

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