1. Equations and Inequalities
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
Chapter 1 Outline

3. Problem Solving and Using Formulas
§ 2.2
Problem Solving and Using Formulas

4. Guidelines for Problem Solving
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. Guidelines for Problem Solving
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.
Carry out the mathematical calculations necessary to solve the problem.

6. Guidelines for Problem Solving
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.
Answer the question. Make sure you have answered the question asked. State the answer clearly in a sentence.

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. Solving Equations Example continued:
We will use the simple interest formula, i=prt. In this problem, p = $5000, r = 0.04, and t = 5.
Solve the equation.
Check: The answer appears reasonable that Arthur will pay $1000 for the use of $5000 for 5 years.
Answer: The simple interest owed is $1000. 

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. Solving Equations Example continued:
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).

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.