1. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.2 – Slide 1

2. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.2 – Slide 2 Equations, Inequalities, and Applications Chapter 2

3. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.2 – Slide 3 2.2 The Multiplication Property of Equality

4. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.2 – Slide 4 Objectives 1.Use the multiplication property of equality. 2.Simplify, and then use the multiplication property of equality. 2.2 The Multiplication Property of Equality

5. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.2 – Slide 5 Multiplication Property of Equality If A, B, and C (C is not equal to 0) represent real numbers, then the equations A = B and AC = BC are equivalent equations. In words, we can multiply each side of an equation by the same nonzero number without changing the solution. 2.2 The Multiplication Property of Equality Using the Multiplication Property of Equality

6. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.2 – Slide 6 Multiply both sides by ⅓. Example 1 Solve. 3x = 42 ⅓ · 3x = ⅓ · 42 x = 14 Check: 3 · 14 = 42 2.2 The Multiplication Property of Equality Using the Multiplication Property of Equality Note: The multiplication property of multiplication also permits dividing each side of an equation by the same nonzero number. Here we could have also solved this equation by dividing both sides by 3 (since this is equivalent to multiplying by ⅓).

7. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.2 – Slide 7 Note In practice, it is usually easier to multiply on each side if the coefficient of the variable is a fraction, and divide on each side if the coefficient is an integer or a decimal. For example, to solve it is easier to multiply by the reciprocal of than to divide by On the other hand, to solve –5x = – 20, it is easier to divide by – 5 than to multiply by 2.2 The Multiplication Property of Equality Using the Multiplication Property of Equality

8. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.2 – Slide 8 Example 2 Solve. (a) –1.5y = 7.5 y = –5 Check: –1.5 · –5 = 7.5 2.2 The Multiplication Property of Equality Using the Multiplication Property of Equality Divide both sides by –1.5.

9. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.2 – Slide 9 Example 3 Solve. 5a – 13a = 56 a = –7 Check: –8 · –7 = 56 2.2 The Multiplication Property of Equality Simplifying and Using the Multiplication Property of Equality First combine like terms. Then solve. – 8a = 56