1. Copyright © 2014, 2010, 2006 Pearson Education, Inc. Section 2.2, Slide 1 Equations, Inequalities, and Applications 2

2. Copyright © 2014, 2010, 2006 Pearson Education, Inc. Section 2.2, Slide 2 1.Use the multiplication property of equality. 2.Simplify, and then use the multiplication property of equality. Objectives 2.2 The Multiplication Property of Equality

3. Copyright © 2014, 2010, 2006 Pearson Education, Inc. Section 2.2, Slide 3 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. Use the Multiplication Property of Equality

4. Copyright © 2014, 2010, 2006 Pearson Education, Inc. Section 2.2, Slide 4 Divide each side by 3. Example 1 Solve. 3x = 42 x = 14 Check: 3 · 14 = 42 Use the Multiplication Property of Equality

5. Copyright © 2014, 2010, 2006 Pearson Education, Inc. Section 2.2, Slide 5 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 Use the Multiplication Property of Equality

6. Copyright © 2014, 2010, 2006 Pearson Education, Inc. Section 2.2, Slide 6 Example 3 Solve. –1.5y = 7.5 y = –5 Check: –1.5 · –5 = 7.5 Use the Multiplication Property of Equality Divide both sides by –1.5.

7. Copyright © 2014, 2010, 2006 Pearson Education, Inc. Section 2.2, Slide 7 Example 5 Solve. Use the Multiplication Property of Equality Multiply each side by the reciprocal.

8. Copyright © 2014, 2010, 2006 Pearson Education, Inc. Section 2.2, Slide 8 Example 7 Solve. 5a – 13a = 56 a = –7 Simplify and Use the Multiplication Property of Equality First combine like terms. Then solve. – 8a = 56