1. Which property is shown in the equation: 3(x + 4) = 3x + 12?

2. The equation 5 + x = x + 5 demonstrates which property?

3. Which equations show the associative property? (Select all that apply)

4. Sarah buys 3 packets of biscuits. Each packet costs $(x + 2). Write an expression for the total cost using the distributive property, then solve if x = $4.

5. A shop offers a discount where you pay $(15 + x) for the first item and $(x + 15) for the second item of the same type. Tom says the total cost is the same regardless of which item is considered "first". Which property explains why Tom is correct?

6. At a fundraiser, students sell tickets in groups. Group A sells (4 + x) + 6 tickets, while Group B sells 4 + (x + 6) tickets. Explain why both groups sold the same number of tickets.

7. Solve the equation using algebraic properties. Show your working and identify which properties you used:

8. Fill in the blanks to complete the equation using the distributive property:

9. Extension: Create your own word problem that requires using the distributive property to solve. Include the solution.

10. Reflection: In one sentence, explain how algebraic properties help make solving equations easier.