Chapter 2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-1 Solving Linear Equations and Inequalities

2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter – 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 Only 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 Chapter Sections

3 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-3 Solving Linear Equations with a Variable on Only One Side of the Equation

4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-4 Equations with a Variable on One Side 1.If the equation contains fractions, multiply both sides by the LCD to eliminate fractions. 2.Use the distributive property to remove parentheses. 3.Combine like terms on the same side of the equation. 4.Use the addition property to obtain an equation with the term containing the variable on one side of the equation and a constant on the other side. This will result in an equation of the form ax = b. 5.Use the multiplication property to isolate the variable. 6.Check the solution in the original equation.

5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-5 Solving Equations Example: Solve the equation 5x – 7 = 13 5x = (Divide both sides by 5) x = 4 Don’t forget to check! 5x = (Add 7 to both sides)

6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-6 Example: Solve the equation x – 0.07x = x = (Divide both sides by 0.93) x = 4 Solving Equations Containing Decimal Numbers or Fractions 0.93x = x = 4.96 (Like terms were combined) 0.93x = 4.96 – x = 4.96 – 1.24 (Subtract 1.24 from both sides) 0.93x = 3.72

7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-7 Helpful Hints and Definitions  To evaluate an expression means to find its numerical value.  To simplify an expression means to perform operations and combine like terms.  To solve an equation means to find the value or the values of the variable that make the equation a true statement.