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.