Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 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 = Copyright © 2015, 2011, 2007 Pearson Education, Inc. 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