https://file.aiquickdraw.com/mathbot/file/1730324798701afoun2s6.jpg

Let's solve each of these expressions step-by-step. 

### Expression 1:
\[
10 - 6 \times 5 \div (2 + 4)
\]
1. Start by solving inside the parentheses:
   \[
   2 + 4 = 6
   \]
2. Next, handle multiplication and division from left to right:
   \[
   6 \times 5 = 30
   \]
   \[
   30 \div 6 = 5
   \]
3. Finally, complete the subtraction:
   \[
   10 - 5 = 5
   \]
**Answer for Expression 1:** \(5\)

---

### Expression 2:
\[
(4 + 8 \div 2 - 6) \times 10
\]
1. Start inside the parentheses and follow the order of operations:
   \[
   8 \div 2 = 4
   \]
2. Substitute back in and continue with the operations inside the parentheses:
   \[
   4 + 4 - 6 = 2
   \]
3. Finally, multiply by 10:
   \[
   2 \times 10 = 20
   \]
**Answer for Expression 2:** \(20\)

---

### Expression 3:
\[
((10 - 6 + 5) \div 9) \times 2
\]
1. Start with the innermost parentheses:
   \[
   10 - 6 = 4
   \]
   \[
   4 + 5 = 9
   \]
2. Now, divide by 9:
   \[
   9 \div 9 = 1
   \]
3. Finally, multiply by 2:
   \[
   1 \times 2 = 2
   \]
**Answer for Expression 3:** \(2\)

---

Would you like further details on any specific step?

---

Here are some related questions for further exploration:
1. What is the order of operations and why is it important in solving expressions?
2. How would the answers change if division and multiplication were swapped in the expressions?
3. How do parentheses affect the result of an expression?
4. What happens if we remove all parentheses from these expressions?
5. Can you create a similar set of expressions with different numbers?

**Tip:** Remember, always perform operations inside parentheses first, followed by division and multiplication, and finally addition and subtraction.

Solve the expressions: 10 - 6 x 5 ÷ (2 + 4), (4 + 8 ÷ 2 - 6) x 10, and ((10 - 6 + 5) ÷ 9) x 2.

Learn how to solve expressions with parentheses and multiple operations using PEMDAS. This problem demonstrates the importance of the order of operations for expressions like 10 - 6 x 5 ÷ (2 + 4), (4 + 8 ÷ 2 - 6) x 10, and ((10 - 6 + 5) ÷ 9) x 2. Suitable for students in Grades 6-8.

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