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

By Lial M.L., Hornsby J.

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We can extend these properties of arithmetic, the inverse properties of addition and multiplication, to the real numbers of algebra. Inverse Properties For any real number a, there is a single real number Ϫa, such that and a ؉ (؊a) ‫ ؍‬0 ؊a ؉ a ‫ ؍‬0. The inverse “undoes” addition with the result 0. 1 For any nonzero real number a, there is a single real number a such that 1 1 aؒ ‫؍‬1 and ؒ a ‫ ؍‬1. a a The inverse “undoes” multiplication with the result 1. The numbers 0 and 1 each have a special property.

A is positive for all positive numbers a. 12. Evaluate each exponential expression. (a) 43 (c) ͑Ϫ4͒3 An Addison-Wesley product. Copyright © 2004 Pearson Education, Inc. 3 Exponents, Roots, and Order of Operations 29 EXERCISES For Extra Help Student’s Solutions Manual MyMathLab InterAct Math Tutorial Software AW Math Tutor Center Decide whether each statement is true or false. If false, correct the statement so it is true. 1. Ϫ46 ෇ ͑Ϫ4͒6 2. Ϫ47 ෇ ͑Ϫ4͒7 3. ͙16 is a positive number. 4. 3 ϩ 5 и 6 ෇ 3 ϩ ͑5 и 6͒ 5.

Multiply both sides by the LCD, 6. Solve ͪ ͩ ͪ ͩ ͪ 6 Step 1 ͩ x ϩ 7 2x Ϫ 8 ϩ ෇ 6͑Ϫ4͒ 6 2 xϩ7 2x Ϫ 8 ϩ6 ෇ 6͑Ϫ4͒ Distributive property 6 2 Multiply. x ϩ 7 ϩ 3͑2x Ϫ 8͒ ෇ Ϫ24 Distributive property x ϩ 7 ϩ 6x Ϫ 24 ෇ Ϫ24 Combine like terms. 7x Ϫ 17 ෇ Ϫ24 Step 3 Add 17. 7x Ϫ 17 ϩ 17 ෇ Ϫ24 ϩ 17 7x ෇ Ϫ7 Combine like terms. 7x Ϫ7 ෇ Step 4 Divide by 7. 7 7 x ෇ Ϫ1 Step 5 Check by substituting Ϫ1 for x in the original equation. x ϩ 7 2x Ϫ 8 ϩ ෇ Ϫ4 6 2 Ϫ1 ϩ 7 2͑Ϫ1͒ Ϫ 8 ϩ ෇ Ϫ4 ? Let x ෇ Ϫ1. 6 2 Ϫ10 6 ϩ ෇ Ϫ4 ?

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