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 kind, quite a few life like examples, wide challenge units, and entire supplementations package deal. in response to its confirmed song list, this revision incorporates a new open layout, extra routines and functions, and extra good points to assist either scholars and teachers be successful.
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Two important properties that are used in producing equivalent equations are the addition and multiplication properties of equality. An Addison-Wesley product. Copyright © 2004 Pearson Education, Inc. 1 Linear Equations in One Variable 51 Addition and Multiplication Properties of Equality Addition Property of Equality For all real numbers A, B, and C, the equations and A؍B A؉C؍B؉C are equivalent. That is, the same number may be added to each side of an equation without changing the solution set.
C) ͱ 9 3 since 16 4 An Addison-Wesley product. Copyright © 2004 Pearson Education, Inc. ͩͪ 3 4 2 9 . 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 find Janet’s speed by substituting the given values of d and t into this formula. d r t 15 3 r Let d 15, t 4 . 3 4 4 3 r 15 и Multiply by the reciprocal of 4 . 3 r 20 Her speed averaged 20 mph. ) Now Try Exercise 25. PROBLEM SOLVING As seen in Example 4, it may be convenient to first solve for a specific unknown variable before substituting the given values. This is particularly useful when we wish to substitute several different values for the same variable. For example, an economics class might need to solve the equation I prt for r to find rates that produce specific amounts of interest for various principals and times.