1.1. Linear Equations
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1 1.1 Linear Equations Basic Terminology of Equations Solving Linear Equations Identities, Conditional Equations, and Contradictions Solving for a Specified Variable (Literal Equations)
2 1.1 Example 1 Solving a Linear Equation (page 85) Solve. Solution set: {6} Copyright 2008 Pearson Addison-Wesley. All rights reserved. 1-2
3 1.1 Example 2 Clearing Fractions Before Solving a Linear Equation (page 85) Solve. Solution set: { 10} Copyright 2008 Pearson Addison-Wesley. All rights reserved. 1-3
4 1.1 Example 3(a) Identifying Types of Equations (page 86) Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. This is a conditional equation. Solution set: {11} Copyright 2008 Pearson Addison-Wesley. All rights reserved. 1-4
5 1.4 Quadratic Equations Solving a Quadratic Equation Completing the Square The Quadratic Formula Solving for a Specified Variable The Discriminant Copyright 2008 Pearson Addison-Wesley. All rights reserved. 1-5
6 1.4 Example 1 Using the Zero-Factor Property (page 111) Solve. 10x² + 5x 4x 2 = 0 5x(2x + 1) 2(2x + 1) = 0 Multiply F & L= -20x² Diff of Middle = +1x 20 1*20 2*10 4*5 or or or Solution set: Copyright 2008 Pearson Addison-Wesley. All rights reserved. 1-6
7 1.4 Example 2 Using the Square Root Property (page 112) Solve each quadratic equation. Since each has x² and no x term use the square root property when solving (a) (b) (c) Copyright 2008 Pearson Addison-Wesley. All rights reserved. 1-7
8 1.4 Example 3 Using the Method of Completing the Square Steps to solving quadratics by completing the square. Rewrite the equation so that the coefficient of x² is one. Re-write the equation such that the constant is alone on one side of the equation and place the plus the blanks on both sides of the equation. Square half the coefficient of x, and add this square to both sides of the equation. In the blank, (½ of b)² Factor the resulting trinomial as a perfect square and combine terms on the other side. Use the square root property to complete the solution. Copyright 2008 Pearson Addison-Wesley. All rights reserved. 1-8
9 1.4 Example 3 Using the Method of Completing the Square, a = 1 (cont.) Solve by completing the square. x² + 10x + = 20 + Solution set: Copyright 2008 Pearson Addison-Wesley. All rights reserved. 1-9
10 1.4 Example 4 Using the Method of Completing the Square, a 1 (page 113) Solve by completing the square. x² + 3 / 2 x + = -5 / 4 + Solution set: Copyright 2008 Pearson Addison-Wesley. All rights reserved. 1-10
11 1.4 Example 5 Using the Quadratic Formula (Real Solutions) (page 115) Solve by the quadratic formula. Write the equation in standard form. a = 1, b = 6, c = 3 Quadratic formula 48 = 16 3 Solution set: Copyright 2008 Pearson Addison-Wesley. All rights reserved. 1-11
12 1.4 Example 6 Using the Quadratic Formula (Nonreal Complex Solutions) (page 115) Solve by quadratic formula. Write the equation in standard form. a = 4, b = 3, c = 5 Quadratic formula Solution set: Copyright 2008 Pearson Addison-Wesley. All rights reserved. 1-12
13 1.4 Example 7 Solving a Cubic Equation (page 116) Solve. Factoring sum/diff of cubes A 3 B 3 = (A B)(A² + AB + B²) A 3 + B 3 = (A + B)(A² AB + B²) or -75 = Solution set: Copyright 2008 Pearson Addison-Wesley. All rights reserved. 1-13
14 1.4 Example 8(a) Solving for a Quadratic Variable in a Formula (page 116) Solve roots. for r. Use ± when taking square Goal: Isolate r. Copyright 2008 Pearson Addison-Wesley. All rights reserved. 1-14
15 1.4 Example 9(a) Using the Discriminant (page 118) Determine the number of distinct solutions, and tell whether they are rational, irrational, or nonreal complex numbers. There is one distinct rational solution. There are two distinct nonreal complex solutions. There are two distinct irrational solutions. Copyright 2008 Pearson Addison-Wesley. All rights reserved. 1-15
16 1.4 Summary Quadratic Equations Solving a Quadratic Equation Completing the Square The Quadratic Formula Solving for a Specified Variable The Discriminant Negative: 2 complex roots Zero: 1 real rational root Positive Perfect square: 2 real rational roots Not a perfect square: 2 real irrational roots Copyright 2008 Pearson Addison-Wesley. All rights reserved. 1-16
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Essentials of College Algebra
Essentials of College Algebra For these Global Editions, the editorial team at Pearson has collaborated with educators across the world to address a wide range of subjects and requirements, equipping students