Transcript Chapter 2-3

Chapter 2
Equations and
Inequalities
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 2-1
1
Chapter Sections
2.1 – Solving Linear Equations
2.2 – Problem Solving and Using Formulas
2.3 – Applications of Algebra
2.4 – Additional Application Problems
2.5 – Solving Linear Inequalities
2.6 – Solving Equations and Inequalities
Containing Absolute Values
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 2-2
2
§ 2.3
Applications of
Algebra
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 2-3
3
Translate a Verbal Statement into an Algebraic
Expression or Equation
Phrase
A number increased by 8
Twice a number
7 less than a number
One-ninth of a number
2 more than 3 times a number
4 less than 6 times a number
12 times the sum of a number
and 5
Algebraic Expression
x+8
2x
x–7
(1/9)x or x/9
3x + 2
6x – 4
12(x + 5)
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 2-4
4
Solving Equations
Example:
Express each phrase as an algebraic expression.
a) the radius, r, decreased by 9 centimeters
b) 5 less than twice the distance, d
c) 7 times a number, n, increased by 8
Solution:
a) r – 9
b) 2d – 5
c)7n + 8
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 2-5
5
Use the Problem-Solving Procedure
Problem-Solving Procedure for Solving Application Problems
1. Understand the problem. Identity the quantity or quantities
you are being asked to find.
2. Translate the problem into mathematical language (express
the problems as an equation).
3. Carry out the mathematical calculations (solve the equation).
4. Check the answer (using the original wording of the
problem).
5. Answer the question asked.
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Chapter 2-6
6
Solving Equations
Example:
FCI Network offers its customers choices of several longdistance calling plans. The Nationwide Plan requires
customers to pay a $5 monthly fee and 8 cents per minute for
any long-distance calls made. The Flat Rate Unlimited Plan
has a $25 monthly fee for unlimited calling—in other words,
there is no per-minute fee. How many minutes of longdistance calls would a customer need to use for the two plans to
cost the same amount?
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 2-7
7
Solving Equations
Understand
We are asked to find the number of minutes of long-distance
calls that would results in both plans having the same total cost.
To solve the problem we will write algebraic expressions for
each plan and then set these expressions equal to each other.
Translate
Let n = number of minutes of long-distance calls.
Then 0.08n = cost for n minutes at 8 cents per minute.
Cost of Nationwide Plan = Cost of Flat Rate Unlimited Plan
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 2-8
8
Solving Equations
Example continued:
Translate
Monthly fee
Cost for n minutes
plus
5
+
Monthly fee
is equal to
0.08n
=
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25
Chapter 2-9
9
Solving Equations
Example continued:
Solve
5  0.08n  25
0.08n  20
0.08n 20

0.08 0.08
n  250
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 2-10
10
Solving Equations
Example continued:
Check the answer
Check: The answer is reasonable and the arithmetic is
easily checked.
Answer: If 250 minutes were used per month, both
plans would have the same total cost.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 2-11
11