1. Solving Equations Unit 5 Lesson 1

2. Solving Equations The development of the equation solving model is based on two ideas. 1.Variables can be isolated by using zero pairs. 2.Equations are unchanged if equivalent amounts are added to each side of the equation.

3. Examining the Tiles Colors and shapes = 1, = x, = -1, = -x, X – 2 = 7 +2 + 2 X = 9

4. Solving One-Step Equations Solve: x - 2 = 7 How can we model this equation? What can we do to isolate the positive x-tile? What is the result? Is it the correct solution? = X = 9 X + 3 = -4 -3 x = -7

5. Solving One-Step Equations Solve: x + 3 = -4 How can we model this equation? What can we do to isolate the positive x-tile? What is the result? Is it the correct solution? = X = -7 2x = -8 2 X = -4

6. Solving One-Step Equations Solve: 2 x = -8 How can we model this equation? We want to get x alone for a solution, but first we need to make two groups of equal tiles on each side of the bar. We can remove all but one set of the tiles from each side. What is the result? = X = -4 -3x = -6 -3 -3 X = 2

7. Solving One-Step Equations Solve: -3x = -6 How can we model this equation? We want to get x alone for a solution, but first we need to make three groups of equal tiles on each side of the bar. We can remove all but one set of the tiles from each side. What is remaining? Therefore, if –x = -2, then what does +x = ? = -X = -2 X = 2