G = (12 × 3 - 6 × 5) ÷ (3 - [2 - (2 × 5 - 12)])

Let's solve the given expression step by step:

\[ G = \frac{(12 \times 3 - 6 \times 5)}{(3 - [2 - (2 \times 5 - 12)])} \]

### Step 1: Solve inside the parentheses

#### Numerator:
\[ 12 \times 3 = 36 \]
\[ 6 \times 5 = 30 \]
\[ 36 - 30 = 6 \]

So, the numerator is \( 6 \).

#### Denominator:
First, handle the innermost parentheses:
\[ 2 \times 5 = 10 \]
\[ 10 - 12 = -2 \]

Now handle the next level of the parentheses:
\[ 2 - (-2) = 2 + 2 = 4 \]

Now, the outer parentheses:
\[ 3 - 4 = -1 \]

So, the denominator is \( -1 \).

### Step 2: Final Calculation

Now, we have:
\[ G = \frac{6}{-1} = -6 \]

### Final Answer:
\[ G = -6 \]

Would you like more details or have any questions?

Here are five related questions for practice:
1. Simplify \( \frac{(15 \times 4 - 8 \times 3)}{(5 - [3 - (4 \times 3 - 6)])} \).
2. Solve \( (25 \times 2 - 6 \times 7) \div (4 - [3 - (10 - 7)]) \).
3. What is the value of \( \frac{(10 \times 6 - 4 \times 3)}{(5 - [3 - (6 \times 4 - 12)])} \)?
4. Calculate \( (9 \times 2 - 5 \times 3) \div (6 - [4 - (3 \times 7 - 15)]) \).
5. Solve \( \frac{(20 \times 3 - 10 \times 2)}{(8 - [7 - (5 \times 3 - 12)])} \).

**Tip:** Always work from the innermost parentheses outward when solving complex expressions with multiple layers of parentheses.

Step-by-step solution for simplifying the algebraic expression (12 × 3 - 6 × 5) ÷ (3 - [2 - (2 × 5 - 12)]). This problem involves using the order of operations and simplifying nested parentheses, suitable for Grades 6-8 students.

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