Algebra for College Students by Margaret L. Lial, John Hornsby, Terry McGinnis

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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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.

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