Chapter 2.pdf - CHAPTER 2 Equations and Inequalities Source Elementary Intermediate Algebra Fourth Edition Prepared and Edited by Dr Mohamad Hammoudi

Chapter 2.pdf - CHAPTER 2 Equations and Inequalities Source...

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CHAPTER 2 Equations and Inequalities Source: Elementary & Intermediate Algebra, Fourth Edition Prepared and Edited by: Dr. Mohamad Hammoudi
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Topics of Chapter 2 2.1: Solving Equations by Adding and Subtracting. 2.2: Solving Equations by Multiplying and Dividing. 2.3:Combining the Rules to Solve Equations. 2.8: Solving Inequalities Using Addition. 2.9: Solving Inequalities Using Multiplication. 2
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2.1: Solving Equations by Adding and Subtracting Objectives: 2.1.1: Determine whether a given number is a solution for an equation 2.1.2: Use the addition property to solve equations 2.1.3: Determine whether a given number is a solution for an application 2.1.4: Translate words to equation symbols 2.1.5: Solve application problems 3
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Equation Definition of Equation An equation is a mathematical statement that two expressions are equal . Some examples are 3 + 4 = 7, x + 3 = 5, P = 2L + 2W. As you can see, an equal sign (=) separates the two equal expressions. These expressions are usually called the left side and the right side of the equation. 4
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Equation An equation may be either true or false. Any number can replace x for the following equation x + 3 = 5 The number 2 is called the solution (or root) of the equation x + 3 = 5 because substituting 2 for x gives a true statement. The set {2} is called the solution set . 5
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Solution and Solution Set Definition of Solution A solution for an equation is any value for the variable that makes the equation a true statement. Definition of Solution Set The solution set for an equation is the set of all values for the variables that make the equation a true statement . Some equations may have more than one solution. Example: x 2 = 9 Solution (3) 2 = 9 and ( 3) 2 = 9 Solution Set = {3, 3} 6
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2.1.1: Determine whether a given number is a solution for an equation Examples: 1. Is 3 a solution for the equation 2 x + 4 = 10? 2. Is a solution of the equation 3 x = 2 x + 1? 3 5 3 2 7
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Degree of Equation The degree of an equation in one variable is the highest power to which the variable is raised. 5 x 4 9 x 2 + 7 x 2 = 0 The highest power to which the x is raised is four . Therefore, it is called a fourth -degree equation. x + 3 = 5 The highest power to which the x is raised is one . Therefore, it is called a first -degree equation or linear equation . This chapter will discuss linear equations. x 2 3 = 6. This is a second -degree equation and is called quadratic equation .
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