By Margaret L. Lial, John Hornsby, Terry McGinnis

The Lial sequence has helped millions of scholars reach developmental arithmetic via its pleasant writing variety, quite a few practical examples, huge challenge units, and entire supplementations package deal. according to its confirmed tune checklist, this revision encompasses a new open layout, extra routines and functions, and extra beneficial properties to aid either scholars and teachers be successful.

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**Sample text**

Notice that 2͑3 ϩ 5͒ 2 и 8 16 and 5 Use the multiplication property of 0. 2 и 3 ϩ 2 и 5 6 ϩ 10 16, so 3 2͑3 ϩ 5͒ 2 и 3 ϩ 2 и 5. 5 2 2 Area of left part is 2 . 3 = 6. Area of right part is 2 . 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.

Explain the distinction between a conditional equation, an identity, and a contradiction. Decide whether each equation is conditional, an identity, or a contradiction. Give the solution set. See Example 5. 53. Ϫ2p ϩ 5p Ϫ 9 3͑ p Ϫ 4͒ Ϫ 5 54. Ϫ6k ϩ 2k Ϫ 11 Ϫ2͑2k Ϫ 3͒ ϩ 4 55. 6x ϩ 2͑x Ϫ 2͒ 9x ϩ 4 56. Ϫ4͑x ϩ 2͒ Ϫ3͑x ϩ 5͒ Ϫ x 57. Ϫ11m ϩ 4͑m Ϫ 3͒ ϩ 6m 4m Ϫ 12 58. 3p Ϫ 5͑ p ϩ 4͒ ϩ 9 Ϫ11 ϩ 15p 59. 7͓2 Ϫ ͑3 ϩ 4r͔͒ Ϫ 2r Ϫ9 ϩ 2͑1 Ϫ 15r͒ 60. 4͓6 Ϫ ͑1 ϩ 2m͔͒ ϩ 10m 2͑10 Ϫ 3m͒ ϩ 8m Decide whether each pair of equations is equivalent.

Let x Ϫ3. Ϫ12 ϩ 6 Ϫ 5 4 Ϫ 18 ϩ 3 ? Multiply. Ϫ11 Ϫ11 True The true statement indicates that ͕Ϫ3͖ is the solution set. Now Try Exercise 13. An Addison-Wesley product. Copyright © 2004 Pearson Education, Inc. 52 CHAPTER 2 Linear Equations, Inequalities, and Applications Notice that in Example 1 the equality symbols are aligned in a column. Do not use more than one equality symbol in a horizontal line of work when solving an equation. NOTE We use the following steps to solve a linear equation in one variable.