Algebraic Expressions and Solving Equations

1. Chapter 2 Equations and Inequalities

2. 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

3. Applications of Algebra § 2.3

4. Translate a Verbal Statement into an Algebraic Expression or Equation

5. 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

6. Use the Problem-Solving Procedure

7. Solving Equations Example: 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?

8. 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

9. Solving Equations Translate Monthly fee Monthly fee is equal to Cost for n minutes plus 5 + 0.08n = 25 Example continued:

10. Solving Equations Solve Example continued:

11. Solving Equations Check the answer Example continued: 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.