The given equation is:

\[
|2x| = 3
\]

This is an absolute value equation. To solve it, we need to consider both the positive and negative cases of the expression inside the absolute value. 

### Steps to solve:

1. **Positive case**:
   \[
   2x = 3
   \]
   Solve for \(x\):
   \[
   x = \frac{3}{2}
   \]

2. **Negative case**:
   \[
   2x = -3
   \]
   Solve for \(x\):
   \[
   x = \frac{-3}{2}
   \]

### Final solution:
\[
x = \frac{3}{2} \quad \text{or} \quad x = \frac{-3}{2}
\]

Would you like more details or have any questions?

Here are five related questions to consider:

1. How do you graph the solution of an absolute value equation?
2. How does the absolute value function affect the outcome of an equation?
3. What are the properties of absolute value equations?
4. Can an absolute value equation ever have no solution?
5. How would you solve the equation \( |ax + b| = c \)?

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

Learn how to solve the absolute value equation |2x| = 3 with a detailed step-by-step guide. This problem introduces absolute value concepts and provides solutions for both the positive and negative cases. Suitable for students in Grades 7-9.

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