Algebra-Geometry I SOLVE: Linear Equations & Inequalities

SUCCESS CRITERIA:1) Solve linear equations. 2) Solve linear inequalities.

3) Solve a system of two linear equations.

4) Solve a system of two linear equalities.

5) Translate real world problem into a system of linear equations or inequalities.

INSTRUCTOR: Craig Sherman Hidden Lake High School

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Trina Northcott Westminster Public Schools

EMPOWER Recorded TARGET SCALE THEME

MA.09.EE.01.04 Expressions can be represented in multiple, equivalent forms

MA.09.EE.02.04 Solving Linear Equations & Inequalities in One Variable

PROFICIENCY SCALE:SCORE REQUIREMENTS

4.0 In addition to exhibiting Score 3.0 performance, in-depth inferences and applications that go BEYOND what was taught in class.

Score 4.0 does not equate to more work but rather a higher level of performance.

3.5 In addition to Score 3.0 performance, in-depth inferences and applications with partial success.

o Determine the appropriate solution in a Real World example.3.0 The learner exhibits no major errors or omissions regarding any of the

information and processes (simple or complex) that were explicitly taught.o Solve linear equations, ANDo Solve linear inequalities ANDo Solve a system of two linear equations, ANDo Solve a system of two linear equalities, ANDo Translate real world problem into a system of linear equations or inequalities.

2.0 Can do one or more of the following skills / concepts: There are no major errors or omissions regarding the simpler details and

processes as the learner…o Understand the key to solving equations is to use the inverse property, ORo Understand the algorithm (step-by-step process) to solve linear

equations, ORo Solve one-step linear equations, OR o Solve two-step linear equations, OR o Solve multi-step linear equations, ORo Solve one-step linear equalities, OR o Solve two-step linear equalities, OR o Solve multi-step linear equalities, ORo Solve a system of two linear equations, ORo Translate real world problems and solve, OR

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o Transform formulas.1.0 Know and use the vocabulary

Identify the Basic ElementsWith help, a partial understanding of some of the simpler details and process

Inverse OperationsWORD or CONCEPT DEFINITION or NOTES EXAMPLE or GRAPHIC REPRESENTATION

linear equation

inverse operation

NOTES:

Classwork

1. Name the inverse operation needed to solve for the variable.

a. x + 9 = 17

b. y – 8 = 5

c. m + 5 = 21

d. w6

=12

e. 9v = 108

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Homework

2. Name the inverse operation needed to solve for the variable.

a. t – 18 = 54

b. 14x = 228

c. m + 19 = 51

d. 11b = 66e. m4=2

One Step Equations

INSTRUCTION 1: KHAN ACADEMY INSTRUCTION 2: SOPHIA

Classwork

3. Solve.

a. n + 7 = 20

b. x + 9 = -8

c. a – 15 = 27

d. y – 21 = -15

e. 50 + w = 92

f. -4 + m = 18

g.m8=16

h. 30 = 12m

i. -5m = 25

j.16t=12

k. -10c = -80

l. n – (-6)= 12

m. -82 + x = -20

n.−r2

=5

Homework

4. Solve.

a. n + 9 = 13

b. -14 + b = 21

c. z – 18 = -14

d. -7 + g = -12

e. 19 = 15 + y

f. b + (-4) = 13

g.q3=33

h. -18x = -360

i. x – 11 = 4

j.15n=15

k. -15c = -75

l. -8 + r = 27

m. 19 + m = 3

n.– w8

=1

Translating and SolvingINSTRUCTION 1: KHAN ACADEMY INSTRUCTION 2: SOPHIA

Classwork

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5. Three more than x is nine

6. The quotient of x and 12 is -2

7. Twice a number is -6

8. Seven less than a number is 84

9. Eight increased by x is 49

Homework

10. Fourteen is six less than a number

11. Three is the same as a number divided by -5

12. The quotient of x and -5 is 10

13. The product of -9 and a number is -81

14. A number subtracted by 37 is 6

Two Step EquationsINSTRUCTION 1: KHAN ACADEMY INSTRUCTION 2: SOPHIA

Classwork

Solve.

15. 7x – 2 = 26

16. ½ (m – 3) = 12

17. -6h – 6 = 30

18. 5x + 20 = -20

19. 3 = -3y – 15

20. -24 = 14y – 5

21. 7r – 5 = 10

22. 9 = 16y + 51

23. 13x + 6 = 6

24. x

−4+11=5

Homework

25. 2m – 8 = -28

26. x

9−3=8

27. 12m + 20 = -40

28−x3

+5=21.

29. 8r – 27 = -19

30. 6+ k

3=33

31. 15 = -4y – 9

32. 8w + 4 = -36

33. 4a – 15 = -23

34. 44 = 5x - 6

Translating and SolvingClasswork

35. Eight more than two times a number is 56

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36. The quotient of a number and four minus 16 is 40

37. 6 times the sum of n and 11 is 30

38. 32 minus twice p is 31

39. Three times a number plus three is forty two

Homework

40. The product of a number and 24, plus three is the same as -21

41. The sum of eighteen and twice a number is equal to ninety

42. Twenty seven less than three times a number is 6

43. Five times number divided into 4 equal parts is the same as 25

44. Three more than the product of a number and six is twenty one

Multi-Step EquationsINSTRUCTION 1: KHAN ACADEMY INSTRUCTION 2: SOPHIA

Classwork

Solve.

45. 8s – (8 + 6s) = 20

46. 34 = 2x + 8(x + 3)

47. 34

( x+9 )=15

48. 23

(m−8 )=4

49. 35 = 22x – 12x + 5

50. 6(b + 8) = 54

51. 99 = 33x + 3(3x + 5)

52. –t + (5t – 7) = -5

53. 21 – 3(2 – w) = -12

54. 9 = 8b – (2b – 3)

Homework

Solve.

55. 6(m + 4) – 2m = -8

56. 44 = 4(8 + h)

57. 3

4(8 t−4 )=−2

58. 0=1

5(10h+15 )+h

59. 3(5 – t) – 4t = 18

60. 2(y - 5) = 16

61. 0.1(h + 20) = 3

62. 3 z8

−4=5

63. 8.6 = 6j + 4j

64. 12z – (4z + 6) = 8

More Equations77. 4x = 24

78. -4 = x - 7

79. x + 2 + x = -2

80. 2(3x + 1) = 32

81. 2(-6 + 4x) = -84

82. -6.5x = -29.25

83. -7x - 6/7 = -63 6/7

84. -3x + 9 - 5x = -47

85. 6(-3x -3) = -54

86. 6(7.7x + 4.3) = 339.96

87. x/ -3 = 6

88. 0 = x - 8

89. 3 + 4x = 31

90. 4 - 6x = -50

91. -29 = x - 7x + 7

92. 3(6x + 7) = 201

93. 7/2 + 3x = 5 9/14

94. -9/4 + 3/2x = 0

95. 5x + 5 - 2x = 5

96. 6.9(1x + 9) = 130.41

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Transforming Formulas

INSTRUCTION 1: KHAN ACADEMY INSTRUCTION 2: SOPHIA

Classwork

97. Solve for w. A = lw

98. Solve for m. t= v+m3

99. Solve for b. 16c−10b=2

100. Solve for h. A=12bh

101. Solve for π. V= 43π r3

Homework

102. Solve for l. P = 2l + 2w

103. Solve for c. p=b+c5

104. Solve for s. 20 x−5 s=8

105. Solve for h. V=2π r2h

106. Solve for h. A=12 (b1+b2 )h

107. The formula for the volume of a right circular cylinder is V = πr2h.The value of h can be expressed as

1) Vπr2 2) πr

2

V

3) Vπ r2 4) V-π r2

108. If c = 2m + d, then m is equal to

1) (c−d)

22) c2−d

3) cd−2 4) d−2c

From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.

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Linear Inequalities: Involving Addition & Subtraction

WORD or CONCEPT DEFINITION or NOTES EXAMPLE or GRAPHIC REPRESENTATION

inequalities

greater than

greater than or equal to

less than

less than or equal to

INSTRUCTION 1: KHAN ACADEMY INSTRUCTION 2: SOPHIA

NOTES:

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Classwork

109. Solve, check and graph the following inequalities.

a. x + 5 > 10b. x + 3 < -2c. 7 > x + 11d. x – 3 ≤ -5e. x – 7 > 3

f. -2 + x ≥ -2g. -9 ≤ x – 3h. x + 0.5 < 4i. -3.75 ≤ x – 1.25j. 8.7 > x + 2.2

110. Write an inequality for each sentence below and then solve and check it.a. The sum of w and nine is less than 18.b. g decreased by 25 is at most five.c. The difference of a number and six is no less than 15.d. 14 is more than the sum of ten and a number.e. 25 plus a number is at least 13.

111. Suppose you must maintain at least $500 in your checking account in order to have free checking. Your balance is $542 and then you write a check for $57. How much do you need to deposit in order to keep your free checking? Write an inequality and solve.

112. You need no more than 2,200 calories in a day. You had 650 calories at breakfast and 825 calories at lunch. At most, how many calories, c can you eat for dinner? Write an inequality and solve.

Homework

113. Solve, check and graph the following inequalities.

a. x + 7 > -2b. x + 3 < -3c. -8 < x + 15d. x – 4 ≤ 1e. x – 1 > 6

f. -7 + x ≥ -11g. -6 ≤ x – 2h. x + 2.5 < 6i. -5.5 ≤ x – 3.25j. 7.9 > x + 4.4

114. Write an inequality for each sentence below and then solve and check it.a. The difference of a number and seven is at most 16.b. 18 is less than a number plus 7c. h decreased by 3 is more than 1.d. 14 is greater than or equal to the sum of 18 and a number.e. The sum of b and 22 is at least 6

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115. Suppose you must maintain at least $500 in your checking account in order to have free checking. Your balance is $612 and then you make a deposit of $79. How much can you withdraw and still keep your free checking? Write an inequality and solve.

116. You need no more than 2,200 calories in a day. You had 720 calories at breakfast and plan on having 1,000 calories at dinner. How many calories, c can you eat for lunch? Write an inequality and solve.

Involving Multiplication and Division

INSTRUCTION 1: KHAN ACADEMY INSTRUCTION 2: SOPHIA

Classwork

117. Solve, check and graph the following inequalities.

a. 5x > -25b. -7x ≤ -21c. 18 > 2xd. 25x ≥ 100

e. -30 ≤ -6xf. 10x < 0g. 8x ≥ 24h. 40 < -8x

i. 20x ≥ 30j. 350 > -70x

118. Solve, check and graph the following inequalities.

a.x5

≥ 2

b.x2 < 14

c. -3 ≤ x−6

d.x

−9 > 1

e.x

−4 ≥ -3

f.x3

≤ 3

g. 0 ≤ x8

h. -1 ≥ x2.5

i.x

−1 < 2.2

j.x

−1.5 > -10

119. Write an inequality for each sentence below and then solve and check it.a. The product of r and 5 is no more than 55.b. The quotient of v divided by -4 is greater than or equal to 2.c. Half of d is greater than 40.d. Twice a number is at most 24.e. One-fourth of y is less than or equal to -12.f. The product of -8 and x is no less than -64.

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120. What happens to the inequality symbol when you do each of the following to both sides of an inequality?a. Multiply by a positive numberb. Divide by a positive numberc. Add a negative numberd. Subtract a negative numbere. Divide by a negative numberf. Multiply by a negative number

Homework

121. Solve, check and graph the following inequalities.

a. 4x ≤ -16b. 32 ≤ 8xc. -7x > 49d. -5x < -55

e. 13x ≥ 0f. 60 < 12xg. 66 > -3xh. -6x ≥ 360

i. -2x ≥ 17j. 26 < 4x

122. Solve, check and graph the following inequalities.

a. 5 ≤ x3

b.x3 < -3

c.x

−8 ≥ 0

d.x3

> 11

e. 4 ≤ x−1

f. -4 ≥ x−6

g.x

−4 ≥ -1.5

h.x4

≤ 12

i.x

−6 > -9

j.x

−2 < 3.3

123. Write an inequality for each sentence below and then solve and check it.a. Four times a number n is no more than 24.b. One-third of m is greater than 9.c. The product of -9 and g is at most 81.d. Half of d is less than or equal to 16.e. The quotient of v divided by -6 is less than 4.f. The product of 7 and x is no less than -42.

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Two-Step and Multi-Step Inequalities

INSTRUCTION 1: KHAN ACADEMY INSTRUCTION 2: SOPHIA

Classwork

124. Solve, check and graph the following inequalities.

a. 10 + 7x < 17

b. -1 + 3x ≥ -28

c. -4x + 2 > -46

d. 3 + 5x + 3x ≤ 19

e. -6x – 6 + 3x > -24

f. -4 – 2x + 5x ≤ 8

g. 6x – 8 > 1 + 3x

h. 3x – 9 > -41 + 7x

i. 4(-7 + 3x) ≥ 32

j. 5(-7x + 8) ≤ 275

k.34

x - 12

≤ −14

l. –x + 67 <

328

125. Write an inequality for each situation, then solve.a. You want to spend $20 for a taxi ride. Before you go anywhere, the taxi driver sets the meter the initial

charge of $2. The meter adds $1.50 for each mile and you plan on giving a $2 tip, what is the farthest you can go?

b. On a trip from New Jersey to Florida, your family wants to travel at least 436 miles in one day from 8am to 5 pm. You plan on only stopping for a total of 1 hour. What must your average speed be?

Homework

126. Solve, check and graph the following inequalities.

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a. 5x + 1 > 51

b. 6x + 6 ≤ 24

c. -6x – 3 > -63

d. 4 – 3x – 5x ≥36

e. 3 + x + 6x < -53

f. 2 + 2x ≤ 3x + 2

g. -8 + 7x ≤ 4x -52

h. 2x + 8 > -x -1

i. 4(-3x -5) < -164

j. 6(3x + 9) ≥ 126

k.23

x + 47

¿ 3142

l. - 14

- 23

x ≤ 5

44

127. Write an inequality for each situation, then solve.a. You have $50 to spend at the boardwalk. Tickets for the rides cost $1.50 and parking is $9. What is

the most number of tickets you can buy?b. You are shopping at the mall and have less than $75 to spend. If you bought 3 shirts and spent $18 on

snacks, how much could one shirt be, is all were the same price?

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SOLVE Linear Equations & Inequalities UNIT REVIEWMultiple Choice– Choose the correct answer for each question.

1. Translate the following three more than the product of six and a number x.

a. 6 + 3x

b. 6x + 3

c. 3x + 6

d. 3 + 6x

2. Translate the following;

The product of the sum of twelve and a number x and the difference a number x and two

a. (12+x) (x-2)

b. (12x)(2x)

c. 12x -2x

d. (12-x)(x+2)

3. Solve the equation: 1 – 9x = 28

a. x = 3

b. x = -3

c. x = 18

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4. Solve the equation: 34 x - 2 = -23

a. p = -21

b. p = 11

c. p = 28

d. p = -28

5. Solve the equation: -2.1k + 13 + 6.5k =24

a. k = 1.26

b. k = - 2.5

c. k = 2.5

d. k = 8.4

6. Solve the equation: - (2d - 11) = -119 a. d = - 54

b. d = 54

c. d = - 65

d. d = 65

7. Which value of x is in the solution set of the inequality 7(x + 1) > -14?

a. -22b. -2c. -1d. 1

Short Constructed Response – Solve each equation and write the correct answer for each question.

8. Solve the equation: 5(x + 10) = - 425 9. 4x + 7 = 38

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10. 55 = 15t + t - 17 11. 12x –43 - 10x = -83

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13. -13(2m - 1) = 65 14. -13 = -4r + 50 + ½ r

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15. Solve and graph: 3x +2 < 0   

16. Translate and solve. The sum of two consecutive integers is 47. What are the two integers?

Extended Constructed Response - Solve the problem, showing all work and explaining each step.

17. Model with an inequality and solve.

Maria is in charge of organizing the school’s holiday carnival. She is setting up booths in the gym. Each booth can have three players. Maria plans on setting up at least 22 booths in the gymnasium. What is the minimum number of players that can compete in the booths at the holiday carnival?

18. Cab Ride Company has trip fee of 2.50 and an additional charge of $0.40 for each 1/5 mile. The Yellow Cab Company has an initial fare of $1.50 and an additional charge of $0.50 for each ¼ m i l e . The S m i t h family is deciding which of these two cab companies to us e .

a. Write an equation that represents the cost of each cab company’s fee. Let c = cost

b. For what number of m i les will the total cost for each of the cab companies be the same?

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c. The Smith family decides to t ak e a 15 m i le t r i p .

(1) Which cab company should they ut i l ize in order to spend less money?

(2) How much money will the Smith’s save in their stay in NY if they have five, fifteen mile trips to take?

19. The Verizon cell phone plan charges a monthly fee of $30 and $0.15/minute. Cingular charges a monthly fee of $25, and $0.20/minute.

A. Write an equation that represents the cost of each cell phone company’s fee. Let c = cost.

B. For what number of minutes will the total cost for each of the cell phone companies be the same?

C. Mary will talk for approximately 150 minutes/month. What plan should she purchase? Explain your answer.

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