Chapter 2 Section 2

The Multiplication Property of Equality 2.2 The Multiplication Property of Equality Use the multiplication property of equality. Simplify, and then use the multiplication property of equality. 2

Use the multiplication property of equality. Objective 1 Use the multiplication property of equality. Slide 2.2-3

Multiplication Property of Equality Use the multiplication property of equality. The addition property of equality is not enough to solve some equations, such as Since the coefficient of x is 3 rather than 1, the multiplication property of equality is needed to change the equation to the form x = a number, after the 2 is subtracted from both sides of the equation and we are left with Multiplication Property of Equality 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 2.2-4

Use the multiplication property of equality. (cont’d) This property can be used to solve . The on the left must be changed to 1x, or x. To isolate x, we multiply each side of the equation by , the reciprocal of 3, which will result in a coefficient of 1 when multiplied. 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. DO NOT, however, divide each side by a variable, since the variable might be equal to 0. 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. Slide 2.2-5

Applying the Multiplication Property of Equality EXAMPLE 1 Applying the Multiplication Property of Equality Solve. Solution: Check: The solution set is Slide 2.2-6

Applying the Multiplication Property of Equality EXAMPLE 2 Applying the Multiplication Property of Equality Solve. Solution: Check: The solution set is Slide 2.2-7

Solving an Equation with Decimals EXAMPLE 3 Solving an Equation with Decimals Solve. Solution: Check: The solution set is Slide 2.2-8

Applying the Multiplication Property of Equality EXAMPLE 4 Applying the Multiplication Property of Equality Solve. Solution: Check: The solution set is Slide 2.2-9

Applying the Multiplication Property of Equality EXAMPLE 5 Applying the Multiplication Property of Equality Solve. Solution: Check: The solution set is Slide 2.2-10

Using the multiplication property of equality when the coefficient of the variable is −1. In Section 2.1, we obtained the equation We reasoned that since this equation says that the additive inverse (or opposite) of x is −17, then x must equal 17. We can also use the multiplication property of equality to obtain the same result as detailed in the next example. Slide 2.2-11

Applying the Multiplication Property of Equality EXAMPLE 6 Applying the Multiplication Property of Equality Solve. Solution: Check: The solution set is Slide 2.2-12

Simplify, and then use the multiplication property of equality. Objective 2 Simplify, and then use the multiplication property of equality. Slide 2.2-13

Combing Like Terms When Solving EXAMPLE 7 Combing Like Terms When Solving Solve. Solution: Check: The solution set is Slide 2.2-14