To solve the equation \( \frac{5x - 2}{3} = 3 - \frac{x}{2} \), we'll follow these steps:

1. **Eliminate the fractions** by finding a common denominator and multiplying both sides of the equation by it. The common denominator for 3 and 2 is 6.

   Multiply every term by 6:
   \[
   6 \cdot \frac{5x - 2}{3} = 6 \cdot \left(3 - \frac{x}{2}\right)
   \]

2. **Simplify** the equation:
   \[
   2(5x - 2) = 6 \cdot 3 - 3x
   \]
   Distribute on both sides:
   \[
   10x - 4 = 18 - 3x
   \]

3. **Combine like terms**:
   Add \(3x\) to both sides to move all \(x\) terms to one side:
   \[
   10x + 3x - 4 = 18
   \]
   Simplify:
   \[
   13x - 4 = 18
   \]

4. **Isolate \(x\)**:
   Add 4 to both sides:
   \[
   13x = 22
   \]
   Divide by 13:
   \[
   x = \frac{22}{13}
   \]

So, the solution is \( x = \frac{22}{13} \).

Would you like more details or have any questions?

Here are five related questions for further practice:

1. Solve \( \frac{7x + 3}{4} = 5 - \frac{2x}{3} \).
2. Solve \( \frac{3x - 4}{2} = 2x + 1 \).
3. Solve \( \frac{5x}{4} - \frac{3}{2} = \frac{2x + 1}{3} \).
4. Solve \( \frac{2x + 5}{6} = \frac{3x - 4}{4} + 1 \).
5. Solve \( \frac{3x + 7}{5} = \frac{4x - 1}{2} \).

**Tip:** When solving equations involving fractions, clearing the fractions by multiplying by the least common denominator (LCD) simplifies the process.

Learn how to solve the equation (5x - 2) / 3 = 3 - x / 2 step-by-step with detailed explanations. This problem involves solving linear equations with fractions, suitable for students in Grades 9-12.

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