Lial M.L., Hornsby J.'s Algebra for College Students PDF

By Lial M.L., Hornsby J.

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Contradiction ͞ None; solution set 0 Final line is false, such as 0 ෇ 1. ) Identity Infinite; solution set {all real numbers} Final line is true, such as 0 ෇ 0. ) EXAMPLE 5 Recognizing Conditional Equations, Identities, and Contradictions Solve each equation. Decide whether it is a conditional equation, an identity, or a contradiction. (a) 5x Ϫ 9 ෇ 4͑x Ϫ 3͒ An Addison-Wesley product. Copyright © 2004 Pearson Education, Inc. 1 5x Ϫ 9 ෇ 4x Ϫ 12 5x Ϫ 9 Ϫ 4x ෇ 4x Ϫ 12 Ϫ 4x x Ϫ 9 ෇ Ϫ12 x Ϫ 9 ϩ 9 ෇ Ϫ12 ϩ 9 x ෇ Ϫ3 Linear Equations in One Variable 55 Distributive property Subtract 4x.

Divide and multiply. Add. (b) 4 и 32 ϩ 7 Ϫ ͑2 ϩ 8͒ Work inside the parentheses first. 4 и 32 ϩ 7 Ϫ ͑2 ϩ 8͒ ෇ 4 и 32 ϩ 7 Ϫ 10 ෇ 4 и 9 ϩ 7 Ϫ 10 ෇ 36 ϩ 7 Ϫ 10 ෇ 43 Ϫ 10 ෇ 33 (c) Add inside parentheses. Evaluate powers. Multiply. Add. Subtract. 1 и 4 ϩ ͑6 Ϭ 3 Ϫ 7͒ 2 Work inside the parentheses, dividing before subtracting. 1 1 и 4 ϩ ͑6 Ϭ 3 Ϫ 7͒ ෇ и 4 ϩ ͑2 Ϫ 7͒ 2 2 1 и 4 ϩ ͑Ϫ5͒ ෇ 2 ෇ 2 ϩ ͑Ϫ5͒ ෇ Ϫ3 Divide inside parentheses. Subtract inside parentheses. Multiply. Add. Now Try Exercises 65 and 71. EXAMPLE 7 Using the Order of Operations 5 ϩ ͑Ϫ23͒͑2͒ .

The term squared comes from the figure of a square, which has the same measure for both length and width, as shown in Figure 15(a). Similarly, the term cubed comes from the figure of a cube. As shown in Figure 15(b), the length, width, and height of a cube have the same measure. 6 6 (b) 6 и 6 и 6 ෇ 6 cubed, or 63 FIGURE EXAMPLE 2 Evaluating Exponential Expressions 15 Write each expression without exponents and evaluate. (a) 52 ෇ 5 и 5 ෇ 25 (b) ͩͪ 2 3 3 ෇ 5 is used as a factor 2 times. 2 2 2 8 и и ෇ 3 3 3 27 2 3 is used as a factor 3 times.

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Algebra for College Students by Lial M.L., Hornsby J.


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