Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 2 Equations, Inequalities and Problem Solving

22 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 1. 3x + 6 = 2x x – 4 a) Is 4 a solution of the eq.? b) Is -3 a solution of the eq.? c) Solve the equation to determine its solution(s)? 2. 6x + 2 – 2x = 4x + 1 a) Is -2 a solution of the eq.? b) Is 6 a solution of the eq.? c) Solve the equation to determine its solution(s)? Yes True statement All real numbers No False statement No solution No Yes 0 = 0 3x + 6 = 3x + 62 = 1 0 = -1

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 2.4 Further Solving Linear Equations

44 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Objectives:  Apply general strategy for solving linear equations  Solve equations containing fractions and decimals  Recognize identities and equations with no solution

55 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solving Linear Equations

66 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: 17 – x + 3 = 15 – (–6) Example 1

77 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: Example 2

88 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: 7(x – 3) = 9x – 7 Example 3

99 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solving Linear Equations Solve:

10 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solving Linear Equations 5x – 5 = 2(x + 1) + 3x – 7 5x – 5 = 2x x – 7 5x – 5 = 5x – 5 Both sides of the equation are identical. Since this equation will be true for every x that is substituted into the equation, the solution is “all real numbers.” True Statement! (-∞, ∞) Infinitely many solutions Identity type of equation which is always true

11 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solving Linear Equations Since no value for the variable x can be substituted into this equation that will make this a true statement, there is “no solution.” 3x – 7 = 3(x + 1) 3x – 7 = 3x + 3 – 7 = 3 3x + ( – 3x) – 7 = 3x + ( – 3x) + 3 False Statement! Contradiction type of equation which is never true

12 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Closure: 1. What are the steps to solve an equation? 2. What is the difference between an identity and a contradiction?