Download - Practice 2.2 Solving Two Step Equations
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1. 2 6y
2 6y Original Equation
622 2y Subtraction Property of Equality
8y Simplify
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2. 5 15x
5 15x Original Equation
5 155 5x Addition Property of Equality
20x Simplify
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3. 14 3m
14 3m Original Equation
14 3 33m Addition Property of Equality
17 m Simplify
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5. 2 20y
2 20y Original Equation
2 0
2 2
2y Division Property of Equality
10y Simplify
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6. 105
y
105
y Original Equation
5105
5y
Multiplication Property of Equality
50 y Simplify
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7. 3 3y
3 3y Original Equation
3 3
3 3
y Division Property of Equality
1 y Simplify
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28. 14
3x
214
3x Original Equation
143
3
2
2 3
2x
Multiplication Property of Equality, reciprocal
21 x Simplify
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9. 5 x
5 x Original Equation
5
1 1
x
Division Property of Equality
5 x Simplify
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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
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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
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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
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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
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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
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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
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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
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20. 3 8 6
t
36
33 8t
116
t
16
6 61t
66t 866
3 6
11 3 8 8 8
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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58. 5 2 3 3 10x x x x 7 3 7x x
3 0
no solution
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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
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60. 2( 3) 2 6j j
2 6 2 6j j
identity
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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
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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
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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
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Solving a Proportion Using the Multiplication Property of Equality
63. 127
8 12
m12
84
8m
21
4m
10.5 m
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64. 4
7 5
x7 7
28
5x
5.6x
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65. 1
5 3
n 33
3
5n
.6 n
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66. 10
3 9
g3 3
10
3g
3.3g
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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
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Solve each proportion using the Cross Products Property
4 871.
3 x
4 24 x 4 24
4 4
x
6 x
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372.
3 5
y
5 9y
5 9
5 5
y
9
5y
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173.
4 10
x
10 4 x
10 4
4 4
x
5
2x
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3 274.
3n
9 2n
9 2
2 2
n
9
2n
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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
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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