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The equation provided is:

\[
|2v - 3| + 12 = 33
\]

We can solve this step by step:

### Step 1: Isolate the absolute value expression
Subtract 12 from both sides:

\[
|2v - 3| = 33 - 12
\]

\[
|2v - 3| = 21
\]

### Step 2: Solve the absolute value equation
The absolute value equation \( |2v - 3| = 21 \) means there are two possible cases:
1. \( 2v - 3 = 21 \)
2. \( 2v - 3 = -21 \)

#### Case 1: \( 2v - 3 = 21 \)
Add 3 to both sides:

\[
2v = 24
\]

Divide by 2:

\[
v = 12
\]

#### Case 2: \( 2v - 3 = -21 \)
Add 3 to both sides:

\[
2v = -18
\]

Divide by 2:

\[
v = -9
\]

### Final solutions:
\[
v = 12 \quad \text{or} \quad v = -9
\]

So the solution is \( v = 12, -9 \).

Would you like more details on any step, or do you have any questions?

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Here are 5 related questions you might find useful:
1. How do you solve equations with absolute value expressions?
2. Can absolute value equations have no solution?
3. What happens if the absolute value expression equals a negative number?
4. How do you solve absolute value inequalities?
5. What are some common applications of absolute value in real-world problems?

**Tip:** Always remember that absolute value represents distance, so it cannot be negative!

Learn how to solve the absolute value equation |2v - 3| + 12 = 33 with a clear, step-by-step solution. This problem utilizes concepts of linear equations and properties of absolute values, suitable for students in Grades 8 to 10.

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