By Margaret L. Lial, John Hornsby, Terry McGinnis
The Lial sequence has helped millions of scholars reach developmental arithmetic via its pleasant writing sort, a number of lifelike examples, vast challenge units, and whole vitamins package deal. based on its confirmed music checklist, this revision encompasses a new open layout, extra routines and purposes, and extra beneficial properties to aid either scholars and teachers prevail.
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2 ϩ 4x͒ Ϫ ͑3 Ϫ 4x͒ ϩ 5 Ϫ͑Ϫ3 ϩ 6x͒ ϩ x ϩ 1 31. 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.
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 Properties of Real Numbers 33 Distributive Property For any real numbers a, b, and c, a(b ؉ c) ؍ab ؉ ac and (b ؉ c)a ؍ba ؉ ca. The distributive property can also be written ab ϩ ac a͑b ϩ c͒ ba ϩ ca ͑b ϩ c͒a. and It can be extended to more than two numbers as well.
6 Ϫ 6x D. 06x 7. Identify each as an expression or an equation. (a) 3x 6 (c) 5x ϩ 6͑x Ϫ 3͒ 12x ϩ 6 (b) 3x ϩ 6 (d) 5x ϩ 6͑x Ϫ 3͒ Ϫ ͑12x ϩ 6͒ 8. Explain why 6x ϩ 9 6x ϩ 8 cannot have a solution. ) An Addison-Wesley product. Copyright © 2004 Pearson Education, Inc. 56 CHAPTER 2 Linear Equations, Inequalities, and Applications Solve and check each equation. See Examples 1 and 2. 9. 7x ϩ 8 1 10. 5x Ϫ 4 21 11. 7x Ϫ 5x ϩ 15 x ϩ 8 12. 2x ϩ 4 Ϫ x 4x Ϫ 5 13. 12w ϩ 15w Ϫ 9 ϩ 5 Ϫ3w ϩ 5 Ϫ 9 14.