3 − [−5 ⋅ 6 − 4 ⋅ (12 : 4 − 5 ⋅ 2) − 24 : 3]


Let's break down the expression step by step:

The expression is:
\[
3 - [-5 \cdot 6 - 4 \cdot (12 \div 4 - 5 \cdot 2) - 24 \div 3]
\]

### Step 1: Simplify within the parentheses

The expression inside the parentheses is:
\[
12 \div 4 - 5 \cdot 2
\]
First, perform the division and multiplication:
\[
12 \div 4 = 3
\]
\[
5 \cdot 2 = 10
\]
Now, subtract:
\[
3 - 10 = -7
\]

Now the expression looks like:
\[
3 - [-5 \cdot 6 - 4 \cdot (-7) - 24 \div 3]
\]

### Step 2: Perform multiplications and divisions

Start with the division and multiplications:
\[
-5 \cdot 6 = -30
\]
\[
4 \cdot (-7) = -28
\]
\[
24 \div 3 = 8
\]

Now the expression becomes:
\[
3 - [-30 - (-28) - 8]
\]

### Step 3: Simplify inside the brackets

Inside the brackets:
\[
-30 - (-28) = -30 + 28 = -2
\]
Now:
\[
3 - [-2 - 8] = 3 - [-10]
\]

### Step 4: Simplify the final expression

\[
3 - [-10] = 3 + 10 = 13
\]

### Final Answer:
\[
\boxed{13}
\]

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

---

Here are 5 related questions to expand on this problem:

1. How would the expression change if the number inside the parentheses was modified?
2. What happens if we switch the signs of the terms inside the brackets?
3. Can you rewrite the expression using only positive numbers?
4. What role do the distributive and associative properties play in solving such expressions?
5. How would the result change if you replaced the division operations with multiplication?

**Tip**: Always follow the order of operations (PEMDAS/BODMAS) when solving complex expressions.

3 − [−5 ⋅ 6 − 4 ⋅ (12 : 4 − 5 ⋅ 2) − 24 : 3]

Learn how to simplify the complex expression 3 − [−5 ⋅ 6 − 4 ⋅ (12 : 4 − 5 ⋅ 2) − 24 : 3] step-by-step, using the order of operations (PEMDAS/BODMAS) and key arithmetic rules. This solution is suitable for students in Grades 6-8.

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