Elementary Algebra by Charles P. McKeague (Auth.) PDF

By Charles P. McKeague (Auth.)

Highly transparent and obtainable, Pat McKeague's best-selling texts supply all of the assessment, drill, and perform scholars have to increase good mathematical talent and self assurance. McKeague's realization to aspect, extraordinary writing kind, and association of mathematical recommendations make educating stress-free and studying available. The 7th version of this renowned sequence supplies the ebook a better emphasis at the connections among equations, tables, and graphs and through incorporating pedagogy that addresses collaborative studying and terminology

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Extra info for Elementary Algebra

Sample text

Two positives: 3(5) = 5 + 5 + 5 = 15 Positive answer 2. One positive: 3(-5) = - 5 + (-5) + (-5) = —15 Negative answer 3. — 3(5) = 5(—3) Commutative property = - 3 + (-3) + (-3) + (-3) + (-3) = —15 Negative answer One negative: 4. Two negatives: — 3(—5) = ? 6 Multiplication of Real Numbers With two negatives, —3(—5), it is not possible to work the problem in terms of repeated addition. ) The answer is probably +15 (that's just a guess), but we need some justification for saying so. We will solve a different problem and in so doing get the answer to the problem (-3X-5).

17. 19. 7(-6) -7(3) -8(2) -3(-l) -ll(-ll) -3(2)(-l) -3(-4)(-5) -6(-D(2) 3(8)(-2) -2(-4)(-3)(-l) 2. 8 ( - 4 ) 4. -5(4) 6. -16(3) 8. - 7 ( - l ) 10. —12(—12) 12. - 2 ( 3 ) ( - 4 ) 14. - 5 ( - 6 ) ( - 7 ) 16. - 1 2 ( 5 ) ( - 1 ) 18. 4(9)(-3) 20. 6 Multiplication of Real Numbers Work the following problems. You may refer to the rule for order of operation. 21. 23. 25. 27. 29. 31. 33. 35. 37. 39. 3(5 - 4) - 2 ( 2 - 5) - 5 ( 8 - 10) -4(6) - 7 -3(-2) - 5 —3(—6) + 4(—1) -3(-2) + (-8)(-6) 2(3) - 3 ( - 4 ) + 4 ( - 5 ) 4(2 + 3) - 5(4 + 7) 2(9 - 8) - 7(5 - 6) 22.

They all say that x is — 1. All three equations are equivalent. The last one is just easier to read. Here are some further examples of how the addition property of equality can be used to solve equations. ▼ Examples Solve the following equations. 4. x - 5 = 12 SOLUTION Since we want x alone on the left side, we choose to add +5 to both sides. x—5 + 5 = 12+5 x + 0 = 17 JC = 17 Addition property of equality 52 Chapter 2 Linear Equations and Inequalities 5. a + 7 = - 3 SOLUTION Since we want a to be by itself, we will add the opposite of 7 to both sides.