Ws Solve Props Commut Assoc

Applying the Commutative and Associative Properties to Algebraic Equations – 2009 Today we will learn how the commutative and associative properties are definted, as well as learn to begin justifying the steps of an equation In order to justify a step of your process, you may use any of the following properties: • Commutative Property (of Addition or Multiplication) — “CP” • Associative Property (of Addition or Multiplication) — “AP” • Substitution — “Sub” • Addition, Subtraction, Multiplication, or Division Properties of Equality — for example “+ P of E” Together: Number and justify each step as you solve the following equations

1. 4x + 3 + 2x = 13

3. 10 − 3x + (−2) = 18

2. 2x + (3 − 4x) = 25

4. 2x+3−4x+6−4x+5−(−2x)+(5−4x) = 28

With a partner, solve and justify each step using a property

1. 2 + 6x − 5 = 58

3. 15x + (3 − 5x) = 10

2. 6 − 3x + 4 − (−5x) = 4(−5)

4. 8 − 4x + 5 − 3x + (5 + 3x) − 5 =

1 2

Solutions Together: Number and justify each step as you solve the following equations

1. 4x + 3 + 2x = 13 4x + 2x + 3 = 13 6x + 3 = 13 6x = 10 2 5 x = or 1 3 3

CP Sub −P of E

(1) (2) (3)

÷P of E

(4)

Sub AP CP Sub −P of E ÷P of E

(5) (6) (7) (8) (9) (10)

2. 2x + (3 − 4x) = 25 2x + (3 + −4x) = 25 2x + 3 + −4x = 25 −4x + 2x + 3 = 25 −2x + 3 = 25 −2x = 22 x = −11 3. 10 − 3x + (−2) = 18 10 + −3x + −2 = 18 10 + −2 + −3x = 18 8 + −3x = 18 −3x = 10 1 10 x = − = −3 3 3

Sub CP Sub −P of E

(11) (12) (13) (14)

÷P of E

(15)

4. 2x + 3 − 4x + 6 − 4x + 5 − (−2x) + (5 − 4x) = 28 2x + 3 + −4x + 6 + −4x + 5 + 2x + (5 + −4x) = 28 2x + 3 + −4x + 6 + −4x + 5 + 2x + 5 + −4x = 28 2x + −4x + −4x + 2x + −4x + 3 + 6 + 5 + 5 = 28 −8x + 19 = 28 −8x = 9 9 1 x = = −1 8 8

Sub AP CP Sub −P of E

(16) (17) (18) (19) (20)

÷P of E

(21)

With a partner, solve and justify each step using a property

1. 2 + 6x − 5 = 58 2 + 6x + −5 = 58 2 + −5 + 6x = 58 −3 + 6x = 58 6x = 61 1 61 = 10 x= 6 6

Sub CP Sub −P of E

(22) (23) (24) (25)

÷P of E

(26)

Sub CP Sub −P of E ÷P of E

(27) (28) (29) (30) (31)

2. 6 − 3x + 4 − (−5x) = 4(−5) 6 + −3x + 4 + 5x = −20 5x + −3x + 6 + 4 = −20 2x + 10 = −20 2x = −30 x = −15 3. 15x + (3 − 5x) = 10 15x + (3 + −5x) = 10 15x + 3 + −5x = 10 15x + −5x + 3 = 10 10x + 3 = 10 10x = 7 7 x= 10 4. 8 − 4x + 5 − 3x + (5 + 3x) − 5 =

Sub AP CP Sub −P of E

(32) (33) (34) (35) (36)

÷P of E

(37)

1 2

1 2 1 8 + −4x + 5 + −3x + 5 + 3x + −5 = 2 1 −4x + −3x + 3x + 8 + 5 + 5 + −5 = 2 1 −4x + 13 = 2

8 + −4x + 5 + −3x + (5 + 3x) + −5 =

1 2 25 25 1 25 1 x = − ÷ −4 = − · − = =3 2 2 4 8 8

−4x = −12

Sub

(38)

AP

(39)

CP

(40)

Sub

(41)

−P of E

(42)

÷P of E

(43)