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
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.
oSolve linear equations, AND
o Solve linear inequalities AND
o Solve a system of two linear equations, AND
o Solve a system of two linear equalities, AND
o 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…
oUnderstand the key to solving equations is to use the inverse property, OR
o Understand the algorithm (step-by-step process) to solve linear equations, OR
o Solve one-step linear equations, OR
o Solve two-step linear equations, OR
oSolve multi-step linear equations, OR
oSolve one-step linear equalities, OR
o Solve two-step linear equalities, OR
oSolve multi-step linear equalities, OR
oSolve a system of two linear equations, OR
oTranslate real world problems and solve, OR
oTransform formulas.
1.0 Know and use the vocabulary
- Identify the Basic Elements
- With help, a partial understanding of some of the simpler details and process
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Inverse Operations
WORD or CONCEPT / DEFINITION or NOTES / EXAMPLE or GRAPHIC REPRESENTATIONlinear equation
inverse operation
NOTES:
Classwork
1. Name the inverse operation needed to solve for the variable.
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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.
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a. t – 18 = 54
b. 14x = 228
c. m + 19 = 51
d. 11b = 66
e. m4=2
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One Step Equations
INSTRUCTION 1: KHAN ACADEMY INSTRUCTION 2: SOPHIA
Classwork
3. Solve.
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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
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Homework
4. Solve.
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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
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Translating and Solving
INSTRUCTION 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
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Homework
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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
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Two Step Equations
INSTRUCTION 1: KHAN ACADEMY INSTRUCTION 2: SOPHIA
Classwork
Solve.
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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
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Homework
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25. 2m – 8 = -28
26. x9-3=8
27. 12m + 20 = -40
28-x3+5=21.
29. 8r – 27 = -19
30. 6+k3=33
31. 15 = -4y – 9
32. 8w + 4 = -36
33. 4a – 15 = -23
34. 44 = 5x - 6
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Translating and Solving
Classwork
35. Eight more than two times a number is 56
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 Equations
INSTRUCTION 1: KHAN ACADEMY INSTRUCTION 2: SOPHIA
Classwork
Solve.
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45. 8s – (8 + 6s) = 20
46. 34 = 2x + 8(x + 3)
47. 34x+9=15
48. 23m-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)
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Homework
Solve.
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55. 6(m + 4) – 2m = -8
56. 44 = 4(8 + h)
57. 348t-4=-2
58. 0=1510h+15+h
59. 3(5 – t) – 4t = 18
60. 2(y - 5) = 16
61. 0.1(h + 20) = 3
62. 3z8-4=5
63. 8.6 = 6j + 4j
64. 12z – (4z + 6) = 8
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More Equations
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77. 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
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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
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Homework
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102. Solve for l. P = 2l + 2w
103. Solve for c. p=b+c5
104. Solve for s. 20x-5s=8
105. Solve for h. V=2πr2h
106. Solve for h. A=12b1+b2h
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107. The formula for the volume of a right circular cylinder is V = π r2h.
The value of h can be expressed as
1) Vπr2 2) πr2V
3) Vπr2 4) V- πr2
108. If c = 2m + d, then m is equal to
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1) (c-d)2 2) 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.
Linear Inequalities: Involving Addition & Subtraction
WORD or CONCEPT / DEFINITION or NOTES / EXAMPLE or GRAPHIC REPRESENTATIONinequalities
greater than
greater than or equal to
less than
less than or equal to
INSTRUCTION 1: KHAN ACADEMY INSTRUCTION 2: SOPHIA
NOTES:
Classwork
109. Solve, check and graph the following inequalities.
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a. x + 5 > 10
b. x + 3 -2
c. 7 x + 11
d. x – 3 ≤ -5
e. x – 7 > 3
f. -2 + x ≥ -2
g. -9 ≤ x – 3
h. x + 0.5 4
i. -3.75 ≤ x – 1.25
j. 8.7 > x + 2.2
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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.
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a. x + 7 > -2
b. x + 3 -3
c. -8 < x + 15
d. x – 4 ≤ 1
e. x – 1 > 6
f. -7 + x ≥ -11
g. -6 ≤ x – 2
h. x + 2.5 < 6
i. -5.5 ≤ x – 3.25
j. 7.9 > x + 4.4
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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 7
c. 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
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.
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a. 5x > -25
b. -7x ≤ -21
c. 18 2x
d. 25x ≥ 100
e. -30 ≤ -6x
f. 10x < 0
g. 8x ≥ 24
h. 40 -8x
i. 20x ≥ 30
j. 350 > -70x
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118. Solve, check and graph the following inequalities.
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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
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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.
120. What happens to the inequality symbol when you do each of the following to both sides of an inequality?