3(x+y) + 2x 3(y+x) + 2x 2x + 3(x+y) (3y + 3x) + 2x 2x + (3x + 3y) (2x +

Aim #7: How do we complete proofs using the properties of
real numbers?
Homework: Handout
Do Now: Fill in the following flow diagram with the correct properties.
3(y+x) + 2x
(3y + 3x) + 2x
3(x+y) + 2x
2x + 3(x+y)
9-16-16
(2x + 3x) + 3y
2x + (3x + 3y)
Fill in the blanks of this proof showing that (w + 5)(w + 2) is
equivalent to w2 + 7w + 10. Write either commutative, associative,
or distributive property in each black.
Homework #6 Solutions: pgs. 18-19 (1-20)
1) D
2) D
3) C
4) A
5) B
6) A
7) Commutative
8) Multiplicative Identity
9) Commutative
10) Additive Identity
12) Associative
13) Commutative 14) Distributive
15) Additive inverse 16) Distributive
Inverse
18) -1
19) 0
20) 0
11) Associative
17) Multiplicative
1) Show that 4y - 8(1 - y) = 12y - 8. Justify each step with a property.
4y - 8(1 - y) ______________________
4y - 8 + 8y _______________________
4y + 8y - 8 _______________________
(4y + 8y) - 8 ______________________
12y - 8
2) Draw a flow diagram and use it to write a proof that (xy)z = (zy)x for all real
numbers x, y, and z.
3) Justify each step with one of the properties of real numbers:
a) 12 + 3(a + 2b) + (-3a)
12 + 3a + 6b + (-3a)
12 + 3a + (-3a) + 6b
12 + 0 + 6b
12 + 6b
Given
__________________________
__________________________
__________________________
__________________________
b) 3x + 5 + (-5) + 2x
3x + 0 + 2x
3x + 2x
5x
Given
__________________________
__________________________
4) Using the Distributive Property, write an equivalent expression to 5(x - 6).
5) Using the Commutative Property, write an equivalent expression for 5(7x).
6) Does the Associative Property work over subtraction? Show an example to
support your answer.
7) What is the additive inverse of -8x? ___________
8) Justify each step with one of the properties of real numbers:
2
2
4
3a (2a + 3) - 2(a + 8) Given
4
2
4
6a + 9a - 2a - 16
_____________________________
4
4
2
6a - 2a + 9a - 16
_____________________________
4
2
4a + 9a - 16
_____________________________
9) Justify each step with one of the properties of real numbers:
2
2x + (5 + 3x)6 - 30
Given
2
2x + 6(5 + 3x) - 30
___________________________
2
2x + 30 + 18x - 30
___________________________
2
2x + 18x + 30 - 30
___________________________
2
2x + 18x + 0
___________________________
2
2x + 18x
_____________________________
10) Write an equivalent expression for -4(5x + 9),
a. Using the Commutative Property of addition. __________________
b. Using the Commutative Property of multiplication. _________________,
11) Using the Associative Property of addition, write an equivalent expression for
3 + [(x + 5) + (x - 6)].
12) Using the Distributive Property, write two equivalent expressions for
3
2
4x - 8x + 4.
Sum It Up!
When writing proofs for solving equations, you must justify each step with a
property.