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Transcript of Equations and Inequalities - Archie HS Math Mrs....
Chapter 1
Equations and
Inequalities
Copyright ©2014 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.1-1
Equations and Inequalities
CHAPTER OUTLINE
1.1 Linear Equations, Formulas and Problem Solving
1.2 Linear Inequalities in One Variable
1.3 Absolute Value Equations and Inequalities
1.4 Complex Numbers
1.5 Solving Quadratic Equations
1.6 Solving Other Types of Equations
1
Copyright ©2014 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-2
Learning Objectives
In Section 1.1 you will see how we can:
A. Solve linear equations using properties of equality
B. Recognize equations that are identities or contradictions
C. Solve for a specified variable in a formula or literal equation
D. Use the problem-solving guide to solve various problem types
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Linear Equations, Formulas and Problem Solving1.1
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Linear Equations, Formulas and Problem Solving1.1
• Day 1: Chapter 1-1
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Assignment:
Pages 82-83
#11-29 odds
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ANSWERS: Pages 82 – 83
# 1 – 3, # 9 – 60 multiples of 3
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ANSWERS: Pages 82 – 83
# 1 – 3, # 9 – 60 multiples of 3
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ANSWERS: Pages 82 – 83
# 1 – 3, # 9 – 60 multiples of 3
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Linear Equations, Formulas and Problem Solving1.1
• Day 2: Chapter 1-1
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Assignment:
Page 83
# 31 – 59 odds
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ANSWERS: Pages 82 – 83
# 1 – 3, # 9 – 60 multiples of 3
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ANSWERS: Pages 82 – 83
# 1 – 3, # 9 – 60 multiples of 3
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ANSWERS: Pages 82 – 83
# 1 – 3, # 9 – 60 multiples of 3
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ANSWERS: Pages 82 – 83
# 1 – 3, # 9 – 60 multiples of 3
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Linear Equations, Formulas and Problem Solving1.1
• Day 3: Chapter 1-1
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Consecutive Integer Word Problems
•The sum of two consecutive integers is
15. Find the numbers.
n + (n + 1) = 15
2n + 1 = 15
2n = 14
n = 7
The exercise did not ask me for the value of the variable
n; it asked for the identity of two numbers. So my answer
is not "n = 7"; the actual answer is:
"The numbers are 7 and 8."
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Consecutive Integer Word Problems
The product of two consecutive negative
even integers is 24. Find the numbers.(n)(n + 2) = 24
n2 + 2n = 24
n2 + 2n – 24 = 0
(n + 6)(n – 4) = 0
Then the solutions are n = –6 and n = 4. Since the numbers I
am looking for are negative, I can ignore the "4" and take n =
–6. Then the next number is n + 2 = –4, and the answer is
The numbers are –6 and –4.
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Consecutive Integer Word Problems
Twice the larger of two numbers is three more
than five times the smaller, and the sum of
four times the larger and three times the
smaller is 71. What are the numbers?
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The point of exercises like this is to give you practice in unwrapping and unwinding these words, and turning
the words into algebraic equations. The point is in the solving, not in the relative "reality" of the problem. That
said, how do you solve this? The best first step is to start labelling:
the larger number: x
the smaller number: y
twice the larger: 2x
three more than five times the smaller: 5y + 3
relationship between ("is"): 2x = 5y + 3
four times the larger: 4x
three times the smaller: 3y
relationship between ("sum of"): 4x + 3y = 71
Now I have two equations in two variables:
2x = 5y + 3
4x + 3y = 71
I will solve, say, the first equation for x:
x = (5/2)y + (3/2)
Then I'll plug the right-hand side of this into the second equation in place of the "x":
4[ (5/2)y + (3/2) ] + 3y = 71
10y + 6 + 3y = 71
13y + 6 = 71
13y = 65
y = 65/13 = 5
Now that I have the value for y, I can solve for x:
x = (5/2)y + (3/2)
x = (5/2)(5) + (3/2)
x = (25/2) + (3/2)
x = 28/2 = 14
As always, I need to remember to answer the question that was actually asked. The solution here is not "x =
14", but is the following sentence:
The larger number is 14, and the smaller number is 5.
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Assignment:
Pages 83 – 84
# 61 – 67 odd
# 69 – 72 all
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ANSWERS:
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ANSWERS:
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ANSWERS:
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Linear Equations, Formulas and Problem Solving1.1
• Day 4: Chapter 1-1
• Worksheets:
– Distance Word Problems
– Mixture Word Problems
– Work Word Problems
Mrs. Carole Del Vecchio from Crest Ridge HS
1. Geometry
2. Motion
3. Mixture
4. Work
5. Investment
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https://www.youtube.com/watch?v=g-VikR3q2nM
https://www.youtube.com/watch?v=34N4G7d55Sc
https://www.youtube.com/watch?v=Pge1KxHOayI
https://www.youtube.com/watch?v=NCqjjoOw3Ckhttps://www.youtube.com/watch?v=hBxSQo--NFI
https://www.youtube.com/watch?v=qHvXlkAx2zg
Mrs. Carole Del Vecchio from Crest Ridge HS
1. Geometry
2. Motion
3. Mixture
4. Work
5. Investment
Copyright ©2014 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.1-45
https://www.youtube.com/watch?v=g-VikR3q2nM
https://www.youtube.com/watch?v=34N4G7d55Sc
https://www.youtube.com/watch?v=Pge1KxHOayI
https://www.youtube.com/watch?v=NCqjjoOw3Ckhttps://www.youtube.com/watch?v=hBxSQo--NFI
https://www.youtube.com/watch?v=qHvXlkAx2zg
Copyright ©2014 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.1-46
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Book Assignment:
Pages 84 – 85
# 73 – 76 all
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Assignment:
Pages 84 – 85
# 73 – 76 all