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By Lial M.L., Hornsby J.

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The table gives the names of these types of equations. Type of Equation Number of Solutions Indication When Solving Conditional One Final line is x ෇ a number. ) Contradiction ͞ None; solution set 0 Final line is false, such as 0 ෇ 1. ) Identity Infinite; solution set {all real numbers} Final line is true, such as 0 ෇ 0. ) EXAMPLE 5 Recognizing Conditional Equations, Identities, and Contradictions Solve each equation. Decide whether it is a conditional equation, an identity, or a contradiction.

A ෇ 1 bh for h 2 (area of a triangle) h r b 1 h͑B ϩ b͒ for B 2 (area of a trapezoid) 15. A ෇ 16. S ෇ 2␲ rh ϩ 2␲ r 2 for h (surface area of a right circular cylinder) b h h B An Addison-Wesley product. Copyright © 2004 Pearson Education, Inc. r 64 CHAPTER 2 Linear Equations, Inequalities, and Applications 9 C ϩ 32 for C 5 (Celsius to Fahrenheit) 5 ͑F Ϫ 32͒ for F 9 (Fahrenheit to Celsius) 17. F ෇ 18. C ෇ 19. When a formula is solved for a particular variable, several different equivalent forms 1 may be possible.

FIGURE 16 This idea is illustrated by the divided rectangle in Figure 16. Similarly, Ϫ4͓5 ϩ ͑Ϫ3͔͒ ෇ Ϫ4͑2͒ ෇ Ϫ8 and Ϫ4͑5͒ ϩ ͑Ϫ4͒͑Ϫ3͒ ෇ Ϫ20 ϩ 12 ෇ Ϫ8, so Ϫ4͓5 ϩ ͑Ϫ3͔͒ ෇ Ϫ4͑5͒ ϩ ͑Ϫ4͒͑Ϫ3͒. These arithmetic examples are generalized to all real numbers as the distributive property of multiplication with respect to addition, or simply the distributive property. An Addison-Wesley product. Copyright © 2004 Pearson Education, Inc. 4 Properties of Real Numbers 33 Distributive Property For any real numbers a, b, and c, a(b ؉ c) ‫ ؍‬ab ؉ ac and (b ؉ c)a ‫ ؍‬ba ؉ ca.

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