To solve the equation \(|2x - 3| = 3x - 2\), we need to consider two cases due to the absolute value.

### Case 1: \(2x - 3 = 3x - 2\)
1. \(2x - 3 = 3x - 2\)
2. Subtract \(2x\) from both sides:
   \[
   -3 = x - 2
   \]
3. Add 2 to both sides:
   \[
   -1 = x
   \]

### Case 2: \(2x - 3 = -(3x - 2)\)
1. \(2x - 3 = -3x + 2\)
2. Add \(3x\) to both sides:
   \[
   5x - 3 = 2
   \]
3. Add 3 to both sides:
   \[
   5x = 5
   \]
4. Divide both sides by 5:
   \[
   x = 1
   \]

Now, we need to verify both solutions in the original equation to ensure they are valid.

#### Verification:
1. For \(x = -1\):
   \[
   |2(-1) - 3| = 3(-1) - 2
   \]
   \[
   |-2 - 3| = -3 - 2
   \]
   \[
   |-5| = -5
   \]
   \[
   5 \neq -5 \quad (\text{Not valid})
   \]

2. For \(x = 1\):
   \[
   |2(1) - 3| = 3(1) - 2
   \]
   \[
   |2 - 3| = 3 - 2
   \]
   \[
   |-1| = 1
   \]
   \[
   1 = 1 \quad (\text{Valid})
   \]

The only solution is \(x = 1\).

Would you like more details or have any questions?

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**Tip:** When solving absolute value equations, always consider both the positive and negative cases for the expression inside the absolute value.

Learn how to solve the equation |2x - 3| = 3x - 2 with detailed step-by-step solutions and verification. This problem covers absolute value equations and linear equations, suitable for Grades 9-12 students.

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