Answer:
Question 6: I know that (8 + 9) + 3 is equal to 8 + (9 + 3) because of the associative property states that you can change the grouping of addends in any order you want. The benefit to using this property is that you can first add numbers that you can combine more easily. For example, (743 + 51) + 49 can be written as 743 + (51 + 49) or 743 + 100. It is more straightforward to add the numbers that equal 100 first and then add the final number.
Question 3: -3(4x + 3) + 5x [Given]; -12x - 9 + 5x [Distributive Property]; -12x + 5x - 9 [Commutative Property]; -7x - 9 [Combine like-terms]. [tex]\frac{1}{2}[/tex] (6k + 10) + 5k [Given]; 3k + 5 + 5k [Distributive Property]; 3k + 5k + 5 [Commutative Property]; 8k + 5 [ Combine like-terms].
Question 4: 4(2 - 5) - 8 = 4 * (-3) - 8 = -12 - 8 = -20; 4 * 2 - 28 = 8 - 28 = -20.
Question 5: 15 * 3 - 2(2 * 3 + 6) = 45 - 2(6 + 6) = 45 - 2(12) = 45 - 24 = 21; 11 * 3 - 12 = 33 - 12 = 21.
