The given equation is:

$|3x - 4| = 2$

Step-by-step solution:

1. Definition of absolute value: The absolute value equation can be broken into two cases: $3x - 4 = 2 \quad \text{or} \quad 3x - 4 = -2$

2. Solving the first case: $3x - 4 = 2$ Add 4 to both sides: $3x = 6$ Divide by 3: $x = 2$

3. Solving the second case: $3x - 4 = -2$ Add 4 to both sides: $3x = 2$ Divide by 3: $x = \frac{2}{3}$

Final solution:

The solution to the equation is: $x = 2 \quad \text{or} \quad x = \frac{2}{3}$

Let me know if you need further details or have any questions.

Related Questions:

1. How would the solution change if the absolute value equation was $|3x - 4| = 5$?
2. What happens if you solve $|x - 1| = 4$ instead?
3. Can you solve $|2x + 3| = 7$? What would the two cases be?
4. How do absolute value inequalities differ from absolute value equations?
5. What are some real-life applications of absolute value equations?

Tip:

Always remember to set up two equations when solving absolute value equations: one for the positive case and one for the negative case.