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 § 2.2 Problem Solving and Using Formulas

4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-4 Guidelines for Problem Solving 1.Understand the problem.  Read the problem carefully at least twice. In the first reading, get a general overview of the problem. In the second reading, determine (a) exactly what you are being asked to find and (b) what information the problem provides.  If possible, make a sketch to illustrate the problem. Label the information given.  List the information in a table if it will help in solving the problem.

5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-5 Guidelines for Problem Solving 2.Translate the problem to mathematical language.  This will generally involve expressing the problem algebraically.  Sometimes this involves selecting a particular formula to use, whereas other times it is a matter of generating your own equation. It may be necessary to check other sources for the appropriate formula to use. 3.Carry out the mathematical calculations necessary to solve the problem.

6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-6 Guidelines for Problem Solving 4.Check the answer obtained in step 3.  Ask yourself: “Does the answer make sense?” “Is the answer reasonable?” If the answer is not reasonable, recheck your method for solving the problem and your calculations.  Check the solution in the original problem if possible. 5.Answer the question. Make sure you have answered the question asked. State the answer clearly in a sentence.

7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-7 Solving Equations Example: Laura Adkins makes a $5000, 4% simple interest personal loan to her friend, Arthur Altshiller, for a period of 5 years. At the end of 5 years, what interest, in dollars, will Arthur pay Laura? Continued.

8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-8 Solving Equations We will use the simple interest formula, i=prt. In this problem, p = $5000, r = 0.04, and t = 5. Solve the equation. Answer: The simple interest owed is $1000. Check: The answer appears reasonable that Arthur will pay $1000 for the use of $5000 for 5 years. Example continued:

9 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-9 Solving Equations Example: Pola Sommers received a holiday bonus of $1350 and invests the money in a certificate of deposit (CD) at a 3.6% annual interest rate compounded monthly for 18 months. How much will the CD be worth in 18 months? Continued.

10 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-10 Solving Equations We will use the compound interest formula,. In this problem, we have p=$1350, r = 3.6%, n = 12 (since there are 12 months in a year), and t = 1.5 (18 months is 1.5 years). Example continued:

11 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-11 Solving Equations Example continued: Check: The answer $ is reasonable, since it is more than Pola originally invested. Answer: Pola’s CD will be worth $ at the end of 18 months.