https://file.aiquickdraw.com/mathbot/file/1729583441309v8x0dg7g.jpg

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.

Learn how to solve the absolute value equation |3x - 4| = 2 with a detailed step-by-step solution. This problem covers key algebraic concepts, including breaking the equation into two cases: 3x - 4 = 2 and 3x - 4 = -2. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation