Practice 2.2 Solving Two Step Equations.

1. 2 6y

2 6y Original Equation

622 2y Subtraction Property of Equality

8y Simplify

2. 5 15x

5 15x Original Equation

5 155 5x Addition Property of Equality

20x Simplify

3. 14 3m

14 3m Original Equation

14 3 33m Addition Property of Equality

17 m Simplify

5. 2 20y


2 0

2 2

2y Division Property of Equality

10y Simplify

6. 105

y

105

y Original Equation

5105

5y

Multiplication Property of Equality

50 y Simplify

7. 3 3y


3 3

3 3

y Division Property of Equality

1 y Simplify

28. 14

3x

214

3x Original Equation

143

3

2

2 3

2x

Multiplication Property of Equality, reciprocal

21 x Simplify

9. 5 x

5 x Original Equation

5

1 1

x

Division Property of Equality

5 x Simplify

Practice 2.2 Solving Two Step Equations

10. 3 2 13y

3 2 13y Original Equation

3 2 132 2y Subtraction Property of Equality

3 15y Simplify

3 1

3 3

5y Division Property of Equality

5y Simplify

11. 5 5 65x

5 5 65x Original Equation


5 70x Simplify

5 0

5 5

7x Division Property of Equality

14x Simplify

214 10

3

x

210

3

x Original Equation

210 3 3

3

x Multiplication Property of Equality

30 2x Simplify


28 x Simplify

115. 8 10

3y

18 10

3y Original Equation

81

8 10 83

y Subtraction Property of Equality

12

3y Simplify

31

23

3y Multiplication Property of Equality

6y Simplify

216. 10

5

x

210

5

x Original Equation

52

05

51x

Multiplication Property of Equality

2 50x Simplify

2 502 2x Subtraction Property of Equality

48x Simplify

Solve each equation. Show all work(KOVACIC WAY)

17. 6 3 18 b 1 6 3 66 8b

3 24 b 3 2

3

3

4b

8 b 6 6

03 Simplify Check

it ( 8) 6 3 18 18 18

18. 3 5 12 x 33 1 3 5 2x

5 15 x 5 1

5

5

5

x

3 x 330

5 Simplify Check

it

(3)3 5 12 12 12

Simplify

20. 3 8 6

t

36

33 8t

116

t

16

6 61t

66t 866

3 6

11 3 8 8 8

23. 6 2 4

k

6 24

6 6 k

8 4

k

84

4 4k

32k 6 2

4

k

2 32

64

8 6 2 2 2

24. 22 8 7 y

822 8 8 7y

14 7 y

14 7

7 7

y

2 y 22 8 ( 2)7

22 8 14 22 22

26. 15 216

x

15 216

15 15x

366

x

66

6 63x

216x 15 216

x

216 15 21

6

15 36 21

21 21

27. 19 8 3

x

19 8 3

19 19x

27 3

x

273 3 3

x

81x 81

19 8 3

19 27 8

8 8

29. 11 8 6 22m m

11 8 6 22m m Original Equation

81 221 6m m Commutative Property of Addition

5 8 22m Combine Like Terms

88 22 85m Addition Property of Equality

5 30m Simplify

5 0

5 5

3m Division Property of Equality

6m Simplify

30. 2 5 5 14y y

2 5 5 14y y

52 145y y

3 5 14y

55 14 53y

3 9y

3 9

3 3

y

3y

Original Equation

Commutative Property of Addition

Combine Like Terms

Subtraction Property of Equality

Simplify


Simplify

32. 15 5(3 10) 5q q

15 5(3 10) 5q q

15 515 50q q

15 10 50q

15 10 50 05 50q

35 10q

35 1

10 0

0

1

q

3.5 q

Original Equation

Distributive Property

Combine Like Terms

Addition Property of Equality

Simplify


Simplify

33. 6(3 5) 66m

6(3 5) 66m Original Equation

18 30 66m Distributive Property

18 30 30 66 30m Subtraction Property of Equality

18 36m Simplify18 36

18 18

m Division Property of Equality

2m Simplify

Solve each equation. SHOW ALL WORK.

35. 5 16 8 10 n n 3 16 10 n

3 16 16 1610 n

Clean BeforeYou Move

(CLT)

1616

0

Clean it up!

3 6 n

3

3 6

3 3

n

2 n 5 16 8( 2) ( 2 10 )

10 16 16 10 10 10

Check IT

37. 34 42 5v v

34 42 4v Combine Line Terms

Subtraction Property of Equality34 442 422 4v

Simplify76 4v

Division Property of Equality76 4

4 4

v

Simplify19 v

34 4219 (19)5

34 34

39. 5( 3) 25 x

Division Property of Equality5

5( 3) 25

5

x

Using Division Property First

Simplify3 5x

Addition Property of Equality3 33 5x

Simplify8x

Division Property of Eq

How about this one:

5( 3) 24 ? Is a good first step?

ua y

litx

5( 3) 24

5 5

x

243

5x

243

53 3x

NOT IN YOU PACKET NOT IN YOUR PACKET

24 15

5 5x

39

5x

40. 2( 10) 12x x

Distributive Property or Division Property of Equality(-2)?

Distributive Property 2x x

Combine Line Terms20 12x

Addition Property of Equality20 20 12 20x

Simplify32x 32x Multiplication Property of

Equality

20 12

Solve each equation. Choose the method you prefer to use.

a a 241.

7 7 7

7 7

2a 2

2a 2

7 7

7 7

2 2

1 a

A second way:

a a 2

77

7 77

a a 7 7 2

7 7

2 a a

2 2 a

2 2

2 2

a

1 a

5 7 42. 6

8 8v

5 5

8

7

8 8

56

8v

26

8v

16

4v

16 46 6

v

1 1

4 6

1

24v

543 9

6 6

y

5 6 9 6

6 6

y

54 5y

54 54 5 54y

59y

59 9 9

6 6

y

5 54

6 6 6

y

59

6 6

y

596 6

6 6

y

59y

545. 6

5 6

x

5 30 6 30

5 6

x 6 25 180x

6 25 25 180 25x

6 155x 6 155

6 6

x

155

6x

5 5 56

5 6 6 6

x

36 5

5 6 6

x

31

5 6

x

315 5

5 6

x

155

6x

47. 4.2 9.1 23.1 x 4.2 23.1 9.1 23.1 23.1 x

27.3 9.1 x 27.3 9.1

9.1 9.1

x

9.1 27.3. ..3

3270

3 x 10 4.2 10 9.1 23. 1x 42 91 231 x

42 231 91 231 231x 271 91x

91 273

271 91

91 91

x

3

3270

3 x

49. 0.52 2.5 5.1y 0.52 2.5 2.5 5.1 2.5y

0.52 2.6y 0.52 2.6

.52 .52

y

.52 2.6. ..5

2600

260

5y

150. Describe two different ways to solve 10 (8 12)

4y

1 1Use distributive property, 10 (8 ) ( 12)

4 4y

Use multiplication property of equality,

1 4( 10) 4 (8 12)

4y

Practice 2.4 Solving Equations with Variables on Each Side

51. 7 2 4 10k k

7 2 4 10k k

7 2 4 4 04 1k kk k

3 2 10k

3 2 102 2k

3 12k

3 1

3 3

2k

4k

Original Equation


Combine Like Terms


Simplify


Simplify

52. 15 22 7 18m m

Original Equation

Addition Property of Equality(variable)

Combine Like Terms


15 22 7 18m m

7 7 15 22 7 18m mm m

22 22 18m

2222 22 22 18m

22 4m Simplify

22

2 4

2

2

2

m Division Property of Equality

2

11m Simplify

53. (5 6) 2(3 8)a a

(5 6) 2(3 8)a a

5 6 6 16a a

5 6 165 6 5a aa a

6 11 16a

6 11 16 61 16a

22 11a

11

22

11

11a

2 a

Original Equation

Distributive Property

Addition Property of Equality(variable)

Combine Like Terms


Simplify


Simplify

55. Describe an equation that is an identity.

book pg 104

An equation that is true for every possible value of the variable.

Example:

1 1x x

56. Describe an equation that has no solution.

book pg 104

If there is no value of the variable that makes the equation true.

Example:

1 2x x

Determine whether each equation is an or whether it has .

identity no solution

57. 4(3 4) 2(6 8) m m

12 16 12 16 m m

identity

58. 5 2 3 3 10x x x x 7 3 7x x

3 0

no solution

59. (3 4) 6 3(3 2) z z z

3 4 6 9 6 z z z

3 4 3 6 z z 3 4 3 3 3 6z zz z

4 6

no solution

60. 2( 3) 2 6j j

2 6 2 6j j

identity

161. 6 3 2

2r r

1 2 6 3 2

2r r

12 6 4 r r

4 4 12 6 4 r rr r 5 12 6r

1212 6 1 5 2r 5 6r 5 6

5 5

r

1

5 1r

62. 6.8 4.2 5.6 3b b

10 6.8 4.2 5.6 3b b

68 42 56 30b b

42 68 42 56 3042b b bb

68 98 30b

68 98 303 030 b

98 98b

98 9

98 8

8

9

b

1 b

2.7 Solving Proportions

A ______________________ is an equation that states that two ratios are equal. proportion

, 0 and 0 a c

b db d

reads:

is to as is to a b c d

Solving a Proportion Using the Multiplication Property of Equality

63. 127

8 12

m12

84

8m

21

4m

10.5 m

64. 4

7 5

x7 7

28

5x

5.6x

65. 1

5 3

n 33

3

5n

.6 n

66. 10

3 9

g3 3

10

3g

3.3g

Solving a Proportion Using the Cross Products Property

Cross - Products

Extremes/Means

, 0 and 0 a c

b db d

and are called cross produ t c sad bccan use cross products to solve proportions

and are called the

and are called t he

a cextremes

b dm

a d

b c eans

Solve each proportion using the Cross Products Property

4 871.

3 x

4 24 x 4 24

4 4

x

6 x

372.

3 5

y

5 9y

5 9

5 5

y

9

5y

173.

4 10

x

10 4 x

10 4

4 4

x

5

2x

3 274.

3n

9 2n

9 2

2 2

n

9

2n

Solve each proportion using any method

8 379.

5 4

b b

4( 8) 5( 3)b b 4 32 5 15b b

4 324 1 45 5b bbb 32 15b

32 15 15 15b 47 b

2 480.

5 6

n n

6 5(2 4)n n 6 10 20n n

6 6 10 20 6n n n n 0 4 20n

20 4 20 20n 20 4n 20 4

4 4

n

5 n

Practice 2.2 Solving Two Step Equations.

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Transcript of Practice 2.2 Solving Two Step Equations.