By Margaret L. Lial, John Hornsby, Terry McGinnis

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**Example text**

To solve the linear equation 8x 2x Ϫ Ϫ13, 3 4 we are allowed to multiply each side by the least common denominator of all the fractions in the equation. What is this least common denominator? 32. 12͑x ϩ 5000͒ 940, we multiply each side by a power of 10 so that all coefficients are integers. What is the smallest power of 10 that will accomplish this goal? 33. Suppose that in solving the equation 1 1 1 x ϩ x x, 3 2 6 you begin by multiplying each side by 12, rather than the least common denominator, 6.

5 = 10. Area of total rectangle is 2(3 + 5) = 16. 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 Review of the Real Number System Properties of Real Numbers The study of any object is simplified when we know the properties of the object.

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. If we solve A 2 bh for h, one possible correct answer is h 2A . b Which one of the following is not equivalent to this? ͩͪ A A. h 2 b ͩͪ 1 B. h 2A b A C. h 1 b 2 1 A 2 D. h b 20. Suppose the formula A 2HW ϩ 2LW ϩ 2LH is solved for L as follows.