advertisement

Chapter 2 Solving Linear Equations and Inequalities Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-1 Chapter Sections 2.1 – Combining Like Terms 2.2 – The Addition Property of Equality 2.3 – The Multiplication Property of Equality 2.4 – Solving Linear Equations with a Variable on One Side of the Equation 2.5 – Solving Linear Equations with the Variable on Both Sides of the Equation 2.6 – Formulas 2.7 – Ratios and Proportions 2.8 – Inequalities in One Variable Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-2 2 Inequalities in One Variable Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-3 3 Inequalities An inequality is a mathematical statement containing one or more inequality sign (<, >, , ). Inequalities x + 3 < 14 x + 4 2x - 6 4 > -x + 3 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-4 4 Properties for Inequalities For all real numbers a, b, and c: 1. If a > b, then a + c > b + c. 2. If a > b, then a - c > b – c. 3. If a > b and c > 0 then ac > bc. b. 4. If a > b and c > 0 then a c c 5. If a > b and c < 0 then ac < bc. b. 6. If a > b and c < 0 then a c c Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-5 5 Solving Inequalities Example: Solve the inequality and graph the solution. x – 5 > -2 x – 5 + 5 > -2 + 5 (Add 5 to both sides) x>3 -3 -2 -1 0 1 2 3 4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-6 6 Solving Inequalities Example: Solve the inequality and graph the solution. 2x + 6 – 2 2x + 6 - 6 – 2 – 6 2x -8 (Subtract 6 from both sides) (Divide both sides by 2) x -4 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-7 7