1. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 9 Equations, Inequalities and Problem Solving

2. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 9.1 The Addition Property of Equality

3. Martin-Gay, Developmental Mathematics, 2e 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Linear Equations An equation is of the form “expression = expression.” x + 7 = 10 An equation contains an equal sign and an expression does not. EquationsExpressions

4. Martin-Gay, Developmental Mathematics, 2e 44 Linear Equations Linear Equation in One Variable A linear equation in one variable can be written in the form Ax + B = C where A, B, and C are real numbers and A ≠ 0. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

5. Martin-Gay, Developmental Mathematics, 2e 55 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Using the Addition Property to Solve Equations Addition Property of Equality Let a, b, and c represent numbers. Then a = bAlso, a = b and a + c = b + cand a – c = b – c are equivalentare equivalent equations.equations.

6. Martin-Gay, Developmental Mathematics, 2e 66 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Solve x – 4 = 7 for x. Check:

7. Martin-Gay, Developmental Mathematics, 2e 77 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Solve: y – 1.2 = –3.2 – 6.6

8. Martin-Gay, Developmental Mathematics, 2e 88 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Solve: 6x + 8 – 5x = 8 – 3

9. Martin-Gay, Developmental Mathematics, 2e 99 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Solve: 3(3x – 5) = 10x

10. Martin-Gay, Developmental Mathematics, 2e 10 Example 4p – 11 – p = 2 + 2p – 20 3p – 11 = 2p – 18 Simplify both sides. p = – 7 Simplify both sides. p – 11 = – 18 Simplify both sides. 3p + ( – 2p) – 11 = 2p + ( – 2p) – 18 Add –2p to both sides. p – 11 + 11 = – 18 + 11 Add 11 to both sides. Solve: Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

11. Martin-Gay, Developmental Mathematics, 2e 11 Example 5(3 + z) – (8z + 9) = – 4z 15 + 5z – 8z – 9 = – 4z Use distributive property. 6 – 3z = – 4z Simplify left side. 6 + z = 0 Simplify both sides. z = – 6 Simplify both sides. 6 – 3z + 4z = – 4z + 4z Add 4z to both sides. 6 + ( – 6) + z = 0 + ( – 6) Add –6 to both sides. Solve: Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.