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X Ϫ3 and x Ϫ3 xϩ3 xϩ3 64. m 1 and 65. k 4 and k 2 16 66. p2 36 and xϩ1 9 8 8 2 mϩ1 mϪ1 mϪ1 p6 An Addison-Wesley product. Copyright © 2004 Pearson Education, Inc. 2 Formulas OBJECTIVES 1 Solve a formula for a specified variable. 2 Solve applied problems using formulas. 3 Solve percent problems. A mathematical model is an equation or inequality that describes a real situation. Models for many applied problems already exist; they are called formulas. A formula is a mathematical equation in which variables are used to describe a relationship.
P Ϫ 2L 2W Step 3 Divide both sides by 2. 2 2 P Ϫ 2L P Ϫ 2L W or W 2 2 Now Try Exercise 9. C A U T I O N In Step 3 of Example 1, you cannot simplify the fraction by dividing 2 into the term 2L. The subtraction in the numerator must be done before the division. P Ϫ 2L PϪL 2 EXAMPLE 2 Solving a Formula with Parentheses The formula for the perimeter of a rectangle is sometimes written in the equivalent form P 2͑L ϩ W͒. Solve this form for W. *Using the distributive property to write ab ϩ ac as a͑b ϩ c͒ is called factoring.
4. Use substitution to decide whether Ϫ2 is a solution of 5͑x ϩ 4͒ Ϫ 3͑x ϩ 6͒ 9͑x ϩ 1͒. If it is not a solution, explain why. 5. The equation 4͓x ϩ ͑2 Ϫ 3x͔͒ 2͑4 Ϫ 4x͒ is an identity. Let x represent the number of letters in your last name. Is this number a solution of this equation? Check your answer. 6. 06͑10 Ϫ x͒͑100͒ is equivalent to which of the following? A. 06x B. 60 Ϫ 6x C. 6 Ϫ 6x D. 06x 7. Identify each as an expression or an equation. (a) 3x 6 (c) 5x ϩ 6͑x Ϫ 3͒ 12x ϩ 6 (b) 3x ϩ 6 (d) 5x ϩ 6͑x Ϫ 3͒ Ϫ ͑12x ϩ 6͒ 8.