By Margaret L. Lial, John Hornsby, Terry McGinnis
The Lial sequence has helped hundreds of thousands of scholars reach developmental arithmetic via its pleasant writing variety, quite a few real looking examples, large challenge units, and whole supplementations package deal. based on its confirmed tune list, this revision contains a new open layout, extra routines and purposes, and extra good points to assist either scholars and teachers be triumphant.
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16. (e) ͙100 10 since 10 2 100. (f) Ϫ͙100 Ϫ10 since the negative sign is outside the radical sign. (g) ͙Ϫ100 is not a real number because the negative sign is inside the radical sign. No real number squared equals Ϫ100. Notice the difference among the expressions in parts (e), (f), and (g). Part (e) is the positive or principal square root of 100, part (f) is the negative square root of 100, and part (g) is the square root of Ϫ100, which is not a real number. Now Try Exercises 37, 41, 43, and 47.
Since each decimal number is given in hundredths, multiply both sides of the equation by 100. 09͑15 Ϫ x͒, by 100, remember the associative property: To multiply three terms, first multiply any two of them. 09͒͑15 Ϫ x͒ becomes 9͑15 Ϫ x͒. 07͑15͒ Multiply each term by 100. 07͑15͒ 6x ϩ 9͑15 Ϫ x͒ 7͑15͒ 6x ϩ 9͑15͒ Ϫ 9x 105 Ϫ3x ϩ 135 105 Ϫ3x ϩ 135 Ϫ 135 105 Ϫ 135 Ϫ3x Ϫ30 Ϫ3x Ϫ30 Ϫ3 Ϫ3 x 10 Distributive property; multiply. Combine like terms. Subtract 135. Divide by Ϫ3. Check to verify that the solution set is ͕10͖.
EXAMPLE 4 Using the Properties of Real Numbers Simplify each expression. (a) 5y Ϫ 8y Ϫ 6y ϩ 11y ͑5 Ϫ 8 Ϫ 6 ϩ 11͒y 2y Distributive property Combine like terms. An Addison-Wesley product. Copyright © 2004 Pearson Education, Inc. 4 (b) 3x ϩ 4 Ϫ 5͑x ϩ 1͒ Ϫ 8 3x ϩ 4 Ϫ 5x Ϫ 5 Ϫ 8 3x Ϫ 5x ϩ 4 Ϫ 5 Ϫ 8 Ϫ2x Ϫ 9 Distributive property Commutative property Combine like terms. (c) 8 Ϫ ͑3m ϩ 2͒ 8 Ϫ 1͑3m ϩ 2͒ 8 Ϫ 3m Ϫ 2 6 Ϫ 3m (d) 3x͑5͒͑y͒ ͓3x͑5͔͒y ͓3͑x и 5͔͒y ͓3͑5x͔͒y ͓͑3 и 5͒x͔y ͑15x͒y 15͑xy͒ 15xy 37 Identity property Distributive property Combine like terms.
Algebra for College Students by Margaret L. Lial, John Hornsby, Terry McGinnis