−2(4−9)−3(−5−32)−6(52−5∗2)/2
 

Let's break down the expression step by step:

Given expression:
\[
-2(4-9) - 3(-5 - 32) - 6\left(\frac{52 - 5 \times 2}{2}\right)
\]

1. **Simplify inside the parentheses:**

   - \( 4 - 9 = -5 \)
   - \( -5 - 32 = -37 \)
   - \( 52 - 5 \times 2 = 52 - 10 = 42 \)

   So, the expression becomes:
   \[
   -2(-5) - 3(-37) - 6\left(\frac{42}{2}\right)
   \]

2. **Multiply the factors:**

   - \( -2(-5) = 10 \)
   - \( -3(-37) = 111 \)
   - \( \frac{42}{2} = 21 \), and \( -6 \times 21 = -126 \)

   Now, the expression simplifies to:
   \[
   10 + 111 - 126
   \]

3. **Combine the results:**

   \[
   10 + 111 = 121
   \]
   \[
   121 - 126 = -5
   \]

So, the value of the expression is \(-5\).

Would you like more details or have any questions?

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Here are five related questions to explore:

1. How do you simplify expressions with nested parentheses?
2. What are the rules for multiplying negative numbers?
3. How do you handle order of operations with division and multiplication?
4. Can you explain how to distribute a negative sign across parentheses?
5. How do you simplify expressions with fractions and whole numbers?

**Tip:** Always follow the order of operations (PEMDAS) when solving expressions: Parentheses, Exponents, Multiplication

Learn how to simplify the arithmetic expression -2(4-9) - 3(-5-32) - 6(52-5*2)/2 step-by-step. This problem covers arithmetic operations with parentheses, negative numbers, and order of operations. Suitable for students in Grades 6-8.

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