Let's solve the given mathematical expression step by step:

$|12 - (4 \times 3 - 6 \div 2)| + 7$

Step 1: Solve inside the parentheses

$4 \times 3 = 12$ $6 \div 2 = 3$ $12 - 3 = 9$

Now, the expression simplifies to:

$|12 - 9| + 7$

Step 2: Evaluate the absolute value

$|3| = 3$

Step 3: Final calculation

$3 + 7 = 10$

Final Answer:

$\boxed{10}$

Would you like me to explain any step in more detail?

Related Questions:

1. How do absolute values work in mathematical expressions?
2. What is the correct order of operations in arithmetic calculations?
3. How does the distributive property apply to expressions with parentheses?
4. What are some real-life applications of absolute values?
5. How do operations inside absolute value signs affect the result?

Tip:

Always solve expressions inside parentheses first and follow the PEMDAS/BODMAS rule to ensure accuracy! 😊