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A. 3x ϩ x Ϫ 1 ෇ 0 B. 8 ෇ x 2 C. 6x ϩ 2 ෇ 9 D. 1 1 xϪ ෇0 2 x 2. Which of the equations in Exercise 1 are nonlinear equations in x? Explain why. 3. Decide whether 6 is a solution of 3͑x ϩ 4͒ ෇ 5x by substituting 6 for x. If it is not a solution, explain why. 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.

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. See Chapter 6. An Addison-Wesley product. Copyright © 2004 Pearson Education, Inc. 2 Formulas 59 One way to begin is to use the distributive property on the right side of the equation to get P ෇ 2L ϩ 2W, which we would then solve as in Example 1.

The solution set, ͕Ϫ3͖, has only one element, so 5x Ϫ 9 ෇ 4͑x Ϫ 3͒ is a conditional equation. (b) 5x Ϫ 15 ෇ 5͑x Ϫ 3͒ Use the distributive property to clear parentheses on the right side. 5x Ϫ 15 ෇ 5x Ϫ 15 0෇0 Subtract 5x and add 15. The final line, 0 ෇ 0, indicates that the solution set is {all real numbers}, and the equation 5x Ϫ 15 ෇ 5͑x Ϫ 3͒ is an identity. (Note: The first step yielded 5x Ϫ 15 ෇ 5x Ϫ 15, which is true for all values of x. ) (c) 5x Ϫ 15 ෇ 5͑x Ϫ 4͒ 5x Ϫ 15 ෇ 5x Ϫ 20 Distributive property 5x Ϫ 15 Ϫ 5x ෇ 5x Ϫ 20 Ϫ 5x Subtract 5x.

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Lehrbuch der algebra by Heinrich Weber


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