To solve the equation \( |3x| - 5 = 7 \), follow these steps:

### Step 1: Isolate the absolute value term
Add 5 to both sides of the equation:

\[
|3x| = 7 + 5
\]
\[
|3x| = 12
\]

### Step 2: Remove the absolute value
The absolute value equation \( |3x| = 12 \) means that \( 3x \) can be either 12 or -12.

Thus, we have two cases:

1. \( 3x = 12 \)
2. \( 3x = -12 \)

### Step 3: Solve both equations
- For \( 3x = 12 \):
  \[
  x = \frac{12}{3} = 4
  \]

- For \( 3x = -12 \):
  \[
  x = \frac{-12}{3} = -4
  \]

### Final Solution:
The two possible values for \( x \) are:
\[
x = 4 \quad \text{or} \quad x = -4
\]

Would you like more details or have any further questions?

Here are 5 related questions:
1. How do you solve equations with absolute values in general?
2. What happens if the number on the right side of the absolute value equation is negative?
3. Can absolute value equations have no solution?
4. How do you graph absolute value functions?
5. What are the applications of absolute value equations in real life?

**Tip**: Always check both the positive and negative cases when solving absolute value equations!

Learn how to solve the absolute value equation |3x| - 5 = 7 with a detailed step-by-step solution. This problem demonstrates how to isolate the absolute value term and solve for both positive and negative cases, applying the absolute value theorem. Suitable for students in Grades 8-10.

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