Chapter 2 Section 2 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

The Multiplication Property of Equality Use the multiplication property of equality. Combine terms in equations, and then use the multiplication property of equality

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 1 Objective 1 Use the multiplication property of equality. Slide

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Use the multiplication property of equality. If, then and represent the same number. Multiplying and by the same number will also result in an equality. The multiplication property of equality states that we can multiply each side of an equation by the same nonzero number without changing the solution. If A, B, and C (C ≠ 0) represent real numbers, then the equations and are equivalent equations. That is, we can multiply each side of an equation by the same nonzero number without changing the solution. Slide Remember the balance analogy from Section 2.1. Whatever we do to one side of the equation, we have to do to the other side to maintain balance.

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley This property can be used to solve. The on the left must be changed to 1x, or x, instead of. To isolate x, we multiply each side of the equation by. We use because is the reciprocal of 3 and. Just as the addition property of equality permits subtracting the same number from each side of an equation, the multiplication property of equality permits dividing each side of an equation by the same number. For example, which we just solved by multiplying each side by, could also be solved by dividing each side by 3. Slide Use the multiplication property of equality. (cont’d)

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley We can divide each side of an equation by the same nonzero number without changing the solution. Do not however, divide each side by a variable, as that may result in losing a valid solution. 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. For example, to solve it is easier to multiply by, the reciprocal of, than to divide by. Slide Use the multiplication property of equality. (cont’d) On the other hand, to solve it is easier to divide by −5 than to multiply by.

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 1 Solve Solution: Dividing Each Side of an Equation by a Nonzero Number Check: The solution set is. Slide

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 2 Solve Solution: Solving an Equation with Decimals Check: The solution set is Slide

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 3 Solution: Using the Multiplication Property of Equality Solve The solution set is Check: Slide

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 4 Solve Using the Multiplication Property of Equality Solution:Check: The solution set is Slide

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley In Section 2.1, we obtained the equation. We reasoned that since this equation says that the additive inverse (or opposite) of k is −17, then k must equal 17. We can also use the multiplication property of equality to obtain the same result as detailed in the next example. Using the multiplication property of equality when the coefficient of the variable is −1 Slide

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 5 Solution: Using the Multiplication Property of Equality when the Coefficient of the Variable is −1 Solve Check: The solution set is Slide

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 2 Objective 2 Combine terms in equations, and then use the multiplication property of equality. Slide

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Solve EXAMPLE 6 Combining Terms in an Equation before Solving Solution:Check: The solution set is Slide