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 type, a variety of reasonable examples, vast challenge units, and entire vitamins package deal. according to its confirmed song checklist, this revision features a new open layout, extra routines and purposes, and extra gains to assist either scholars and teachers be triumphant.
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Thus, 4 and 41 are multiplicative inverses, as are Ϫ 23 and Ϫ 32 . ) 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.
FIGURE 1 Solve the formula P 2L ϩ 2W for W. This formula gives the relationship between the perimeter (distance around) a rectangle, P, the length of the rectangle, L, and the width of the rectangle, W. See Figure 1. Solve the formula for W by getting W alone on one side of the equals sign. To begin, subtract 2L from both sides. P 2L ϩ 2W Step 1 Subtract 2L. P Ϫ 2L 2L ϩ 2W Ϫ 2L P Ϫ 2L 2W Step 2 is not needed here. P Ϫ 2L 2W Step 3 Divide both sides by 2. 2 2 P Ϫ 2L P Ϫ 2L W or W 2 2 Now Try Exercise 9.
We can substitute different numbers of tickets to get the costs to purchase those tickets. EXAMPLE 8 Evaluating Algebraic Expressions Evaluate each expression if m Ϫ4, n 5, p Ϫ6, and q 25. (a) 5m Ϫ 9n Replace m with Ϫ4 and n with 5. 5m Ϫ 9n 5͑Ϫ4͒ Ϫ 9͑5͒ Ϫ20 Ϫ 45 Ϫ65 m ϩ 2n Ϫ4 ϩ 2͑5͒ Ϫ4 ϩ 10 6 1 Ϫ (b) 4p 4͑Ϫ6͒ Ϫ24 Ϫ24 4 (c) Ϫ3m3 Ϫ n2͑ ͙q ͒ Ϫ3͑Ϫ4͒3 Ϫ ͑5͒2͑ ͙25 ͒ Ϫ3͑Ϫ64͒ Ϫ 25͑5͒ 192 Ϫ 125 67 Substitute; m Ϫ4, n 5, and q 25. Evaluate powers and roots. Multiply. Subtract.