Practice Page
Decide upon your answer and then check the "Explanation" drop down.

1. Explain why the following statements are equivalent: 4(x + y) = 4x + 4y
 


2. Rewrite this expression using the Distributive Property: 6x + 12
 


3. Using the Distributive Property, write an expression equivalent to 5(x - 6).
 


4. Rewrite this expression using the Distributive Property: -5x - 25
 


5. Explain why the following statements are equivalent: a + (b + 4) = a + (4 + b)
 


6. Using the Commutative Property, write an equivalent expression for 5•(7x).
 


7. Explain why the following equation is true: (x + 4) + (-x + (- 4)) = 0.
 


8. Simplify this expression and justify your steps: 12 + 3(a + 2b) - 2a - 3b - 9 + b
 
(The Explanation shown below is one possible solution.)
 
12 + 3(a + 2b) - 2a - 3b - 9 + b        
 
12 + 3a + 6b - 2a - 3b - 9 + b
 
12 - 9 + 3a - 2a + 6b - 3b + b
 
(12 - 9) + (3a - 2a) + (6b - 3b + b)
 
(3) + (3a - 2a) + (6b - 3b + b)
 
3 + a(3 - 2) + b(6 - 3+ 1)
 
3 + a(1) + b(4)
 
3 + a + 4b

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