Here's how to complete the worksheet by filling in the blanks with the correct properties or operations:

1. Given: $3x + (32 + 5x) - 25$
2. Step 5: $3x + (5x + 32) - 25$ → Commutative Property (Reordering terms inside the parentheses)
3. Step 6: $(3x + 5x) + (32 - 25)$ → Associative Property (Regrouping terms)
4. Step 7: $8x + 7$ → Combine Like Terms (Adding $3x + 5x = 8x$ and simplifying $32 - 25 = 7$)
5. Step 8: $10 + 2(3x - 7)$ → Given
6. Step 9: $10 + 6x - 14$ → Distributive Property (Expanding $2(3x - 7) = 6x - 14$)
7. Step 10: $6x - 14 + 10$ → Commutative Property (Reordering terms)
8. Step 11: $6x - 4$ → Combine Like Terms (Simplifying $-14 + 10 = -4$)

Would you like a deeper explanation of any step?

Related Questions:

1. What is the difference between the associative and commutative properties?
2. How does the distributive property work with negative numbers?
3. Can you provide an example where the inverse property is used?
4. Why is it important to follow the order of operations when simplifying expressions?
5. How can the identity property be useful in algebraic manipulations?

Tip: Always simplify expressions step by step, checking for applicable properties to make the process easier!