1. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Mrs. Rivas International Studies Charter School. Bell Ringer

2. Chapter 2 Section 1

3. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. The Addition Property of Equality Identify linear equations. Use the addition property of equality. Simplify, then use the addition property of equality. 2.1 2 3

4. Copyright © 2012, 2008, 2004 Pearson Education, Inc. An equation is a statement asserting that two algebraic expressions are equal. Slide 2.1-3 Definitions. Equation Remember that an equation (to solve) includes an equals symbol which distinguishes is from an expression (to simplify or evaluate). Expression A solution of an equation is a number that makes the equation true when it replaces the variable. An equation is solved by finding it solution set, the set of all solutions. Equations with exactly the same solution sets are equivalent equations.

5. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 1 Identify linear equations. Slide 2.1-4

6. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Linear Equation in One Variable A linear equation in one variable can be written in the form where A, B, and C are real numbers, and with A ≠ 0. Linear Equations Nonlinear Equations Slide 2.1-5 Identify linear equations. The simplest type of equation is a linear equation.

7. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 2 Use the addition property of equality. Slide 2.1-6

8. Copyright © 2012, 2008, 2004 Pearson Education, Inc. To solve an equation, add the same number to each side. The justifies this step. Addition Property of Equality If A, B, and C are real numbers, then the equations and are equivalent equations. That is, we can add the same number to each side of an equation without changing the solution. Equations can be thought of in terms of a balance. Thus, adding the same quantity to each side does not affect the balance. Slide 2.1-7 Use the addition property of equality.

9. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: The solution set is. The final line of the check does not give the solution to the problem, only a confirmation that the solution found is correct. Do NOT write the solution set as {x = 9}. This is incorrect notation. Simply write {9}. Check: Solve. Slide 2.1-8 EXAMPLE 1 Applying the Addition Property of Equality

10. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: The solution set is. Check: Solve. Slide 2.1-9 EXAMPLE 2 Applying the Addition Property of Equality

11. Copyright © 2012, 2008, 2004 Pearson Education, Inc. The addition property of equality says that the same number may be added to each side of an equation. The same number may be subtracted from each side of an equation without changing the solution. In Section 1.5, subtraction was defined as addition of the opposite. Thus, we can also use the following rule when solving an equation. Slide 2.1-10 Use the addition property of equality. (cont’d)

12. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Solve. Check: The solution set is. Slide 2.1-11 EXAMPLE 3 Applying the Addition Property of Equality

13. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Solve. Check: The solution set is. Slide 2.1-12 EXAMPLE 4 Subtracting a Variable Expression

14. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: The solution set is. Check: Solve. Slide 2.1-13 EXAMPLE 5 Applying the Addition Property of Equality Twice

15. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 3 Simplify, and then use the addition property of equality. Slide 2.1-14

16. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Solve. Check: The solution set is. Slide 2.1-15 EXAMPLE 6 Combining Like Terms When Solving

17. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Check: The solution set is. Solve. Be careful to apply the distributive property correctly, or a sign error may result. Slide 2.1-16 EXAMPLE 7 Using the Distributive Property When Solving