3 6 Solving Equations Using the Balancing Method

3. 6 – Solving Equations Using the Balancing Method We’ll learn symbolic methods to solve equations.

Balancing Method �Working backward to “undo” operations is a symbolic method that gives exact solutions. �Another symbolic method that you can apply to solve equations is the balancing method. �In the investigation, we will discover how to use the balancing method. �We’ll realize that the balancing method is very similar to the undoing method.

Investigation: Balancing Pennies �Please complete the following investigation �Investigation 3. 6, pages 80 - 82

The Additive Inverse �An actual balance scale cannot model equations with negative numbers. �The idea of balancing equations involving negative numbers is possible. �Remember, when we add any number to its opposite, we get zero. �The opposite of a number is called the additive inverse because opposite numbers added together is always zero.

Additive Inverse Examples

Multiplicative Inverse �The multiplicative inverse is similar to the additive inverse except that instead of adding to get zero, we are multiplying to get 1. Examples:

Example A: Draw a series of balance-scale pictures to solve the equation Hint: The goal is to end up with a single x -cup on one side of the balance scale. Why can we add 6+2 together and not -2+4 x? 6 and 2 are like terms. Like terms are terms in which the variable component is the same, and they may differ only by a coefficient.

Copy and fill in the table to solve the equation as in example A. Picture Action Taken Original equation. Add 2 to both sides. Divide both sides by 2. Reduce. Equation

Example B: Solving Using Balancing �Mathematics is a foreign language so we need to explain each step as if we’re teaching someone how to get the answer. Do this by making a math/words table. Math Words Original equation. Add 10 to both sides of the equation. Divide both sides of the equation by 3. x equals 5.

Solve using the balancing method. Try this on your own. Math Words Original equation. Add 2 to both sides of the equation. Multiply both sides of the equation by 6. x equals 78.

Homework � 3. 6 Practice Worksheet, page 6