https://file.aiquickdraw.com/mathbot/file/1726178861934jmmlby11.jpg

The equation provided in the image is:

\[
3 |2x - 6| + 2 = 2
\]

### Step-by-Step Solution:

1. **Isolate the Absolute Value Term:**

   Subtract 2 from both sides to isolate the absolute value:

   \[
   3 |2x - 6| = 0
   \]

2. **Divide by 3:**

   To solve for the absolute value, divide both sides by 3:

   \[
   |2x - 6| = 0
   \]

3. **Solve the Absolute Value Equation:**

   The absolute value of a number is 0 only if the number itself is 0. Therefore:

   \[
   2x - 6 = 0
   \]

4. **Solve for \( x \):**

   Add 6 to both sides:

   \[
   2x = 6
   \]

   Divide by 2:

   \[
   x = 3
   \]

### Solution:

The solution to the equation is:

\[
\boxed{x = 3}
\]

Would you like more details or have any questions?

### Related Questions:

1. How do you solve absolute value equations with more than one solution?
2. What happens if there is no solution for an absolute value equation?
3. How do you graph an absolute value function?
4. What are some applications of absolute value equations in real life?
5. How do you solve absolute value inequalities?

**Tip:** Remember that the absolute value equation \( |A| = B \) has no solution if \( B < 0 \), as absolute values cannot be negative.

Learn how to solve the absolute value equation 3|2x - 6| + 2 = 2. This step-by-step solution covers key algebraic concepts, including absolute value properties and solving linear equations. Suitable for students in Grades 7-9.

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