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Equations and Inequalities

Enhance your math skills in solving linear equations and inequalities. Learn to apply formulas to real-world problems effectively. Develop problem-solving strategies and validate solutions. Improve mathematical reasoning and accuracy.

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Equations and Inequalities

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  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. Problem Solving and Using Formulas § 2.2

  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 $1424.79 is reasonable, since it is more than Pola originally invested. Answer: Pola’s CD will be worth $1424.79 at the end of 18 months.

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