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

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 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

Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-3 Combining Like Terms

Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-4 Adding with Same Signs To add real numbers with the same sign, add their absolute values. The sum has the same sign as the numbers being added. Example: –12 + (–3) = – = 34 The sum of two positive numbers will always be positive and the sum of two negative numbers will always be negative.

Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-5 Adding with Different Signs To add real numbers with the different signs, subtract the smaller absolute value from the larger absolute value. The sum has the sign of the number with the larger absolute value. Example: 12 + (–3) = 9– = 4 The sum of two numbers with different signs may be positive or negative. The sign of the sum will be the same as the sign of the number with the larger absolute value.

Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-6 The parts in an algebraic expression that are added are called the terms of the expression. Expression -2x + 3y - 8 3y 2 - 2x + Terms -2x, 3y, -8 3y 2, -2x, Terms

Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-7 The numerical part of a term is called its numerical coefficient or coefficient. Numerical Coefficient Term 5x 7 4(x-3) Terms

Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-8 Like terms are terms that have the same variables with the same exponents. Like Terms 3x, -4x 4y, 6y Unlike Terms 3x, 2 3x, 4y Like Terms

Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-9 Combining Like Terms 1.Determine which terms are like terms. 2.Add or subtract the coefficients of the like terms. 3.Multiply the number found in step 2 by the common variable(s). Example: 6.47b – 8.39b = -1.92b

Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-10 Distributive Property For any real numbers a, b, and c, a(b + c) = ab + bc Example: 2(x + 4) = 2x + 8

Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-11 Simplifying an Expression 1.Use the distributive property to remove any parentheses. 2.Combine like terms. Example: Simplify 6 + 2(4x + 9) = 6 + 8x + 18 (Distributive Property) = 8x + 24(Combined Like Terms) (Note: 8x + 24 is the same as x; however, we generally write the term containing the variable first.