To solve the equation \( |3x - 5| = 3 \), we must consider the definition of absolute value. An absolute value equation \( |A| = B \) has two possible solutions: 

1. \( A = B \)
2. \( A = -B \)

In this case, \( A = 3x - 5 \) and \( B = 3 \). So, the two cases are:

### Case 1: 
\[
3x - 5 = 3
\]
Solving for \( x \):
\[
3x = 3 + 5
\]
\[
3x = 8
\]
\[
x = \frac{8}{3}
\]

### Case 2: 
\[
3x - 5 = -3
\]
Solving for \( x \):
\[
3x = -3 + 5
\]
\[
3x = 2
\]
\[
x = \frac{2}{3}
\]

Thus, the two solutions are:
\[
x = \frac{8}{3} \quad \text{or} \quad x = \frac{2}{3}
\]

Would you like more details on this process or explanations about absolute value equations?

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Here are 5 related questions to explore:

1. How would you solve \( |2x + 7| = 5 \)?
2. What happens if \( |4x - 3| = -2 \)? Can an absolute value be negative?
3. How do you graph the equation \( |x - 1| = 3 \)?
4. How do you solve absolute value inequalities like \( |x - 2| \leq 4 \)?
5. What is the general form of an absolute value equation?

**Tip:** Always check both solutions in the original equation when solving absolute value problems to avoid extraneous solutions.

Discover how to solve the absolute value equation |3x - 5| = 3 with a clear, step-by-step solution. This problem explores algebraic concepts, including the properties of absolute value equations and their solutions. Ideal for students in Grades 9-11.

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