practice 2.2 solving two step equations
Post on 21-Jan-2016
229 Views
Preview:
TRANSCRIPT
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 20y Original Equation
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 3y Original Equation
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
55 65 55x Addition Property of Equality
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
30 22 2x Addition Property of Equality
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
Division Property of Equality
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
Division Property of Equality
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
Subtraction Property of Equality
Combine Like Terms
Subtraction Property of Equality
Simplify
Division Property of Equality
Simplify
52. 15 22 7 18m m
Original Equation
Addition Property of Equality(variable)
Combine Like Terms
Subtraction Property of Equality
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
Subtraction Property of Equality
Simplify
Division Property of Equality
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
top related