1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-1 Equations and Inequalities Chapter 2

2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter – 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 Chapter Sections

3 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-3 § 2.3 Applications of Algebra

4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-4 Translate a Verbal Statement into an Algebraic Expression or Equation PhraseAlgebraic Expression A number increased by 8x + 8 Twice a number2x 7 less than a numberx – 7 One-ninth of a number(1/9)x or x/9 2 more than 3 times a number3x less than 6 times a number6x – 4 12 times the sum of a number and 5 12(x + 5)

5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-5 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 – 9b) 2d – 5c)7n + 8 Solving Equations Example:

6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-6 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.

7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-7 FCI Network offers its customers choices of several long- distance 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 long- distance calls would a customer need to use for the two plans to cost the same amount? Solving Equations Example:

8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-8 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 Solving Equations

9 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-9 Translate Monthly fee 5 Cost for n minutes 0.08n plus + is equal to = 25 Monthly fee Solving Equations Example continued:

10 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-10 Solve Solving Equations Example continued:

11 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-11 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. Solving Equations Example continued: