304 CHAPTER 6 Algebra, Graphs, and Functions Exercises Warm Up Exercises In Exercises 1–10, fill in the blank with an appropriate word, phrase, or symbol(s). 1. A letter of the alphabet used to represent numbers is called a(n) ___________. Variable 2. A symbol that represents a specific quantity is called a(n) ___________. Constant 3. A collection of variables, numbers, grouping symbols, and operation symbols is called an algebraic ___________. Expression 4. The number or numbers that replace the variable to make an equation a true statement is called the ___________ to the equation. Solution 5. The parts that are added or subtracted in an algebraic expression are called ___________. Terms 6. Terms that have the same variables with the same exponents on the variables are called ___________ terms. Like 7. The numerical part of a term is called its numerical ___________. Coefficient 8. An equation in which the highest exponent on the variable is a 1 is called a(n) ___________ equation. Linear 9. An equation that is true for all real numbers is called a(n) ___________. Identity 10. An equation that has no solution is called a(n) ___________. Contradiction Practice the Skills In Exercises 11–26, combine like terms. 11. + x x 4 9 x 13 12. − x x 8 5 x3 13. − + − x x 7 3 8 x4 8 − − 14. − − + x x 9 2 15 − + x 11 15 15. x y x y 7 3 4 8 + − + + x y 3 11 16. − + + − y z y z 5 4 2 9 − − y z 3 5 17. − + − − − x y x y 5 7 8 3 11 13 − − x y 2 18 5 18. x y x y 13 5 21 6 3 24 − − − + + − + x y 7 2 3 19. x x x x 7 3 9 4 8 2 2 − + − + − − x x 6 17 2 − − − 20. − − + + − − x x x x 13 3 23 4 29 2 2 − − − x x 9 4 6 2 21. − − − r r 2( 7) 10( 2) − + r8 6 22. − − + + r r 6( 3) 2( 5) 10 − r4 18 23. − + x x 6.2 8.3 7.1 − x 13.3 8.3 24. − + x x 4.7 6.1 8.2 − x 12.9 6.1 25. + − x x 3 5 3 10 8 − x 9 10 8 26. − − x x 1 5 1 3 4 − − x 2 15 4 In Exercises 27–38, evaluate the expression for the given value(s) of the variable(s). 27. − = x x 5 9, 4 11 28. − = − x x 4 3, 1 −7 29. − + = − x x 3 7, 2 13 30. x x 5, 6 − − = − 1 31. = x x , 8 2 64 32. = − x x , 3 2 9 33. − = − x x , 5 2 −25 34. − = x x , 1 2 −1 35. − + = x x x 5 12, 3 2 6 36. x x x 7 3, 4 2 + − = − −15 37. − + − = − x x x 3 10, 2 2 −20 38. − + − = x x x 2 5 9, 3 2 −12 In Exercises 39– 44, determine whether the given value is a solution to the equation. 39. + = = x x 4 5 17, 3 Yes 40. x x 7 1 29, 4 − = − = − Yes 41. − = + = − x x x 8 7 5 1, 2 No 42. + = − = x x x 4 3 7 6, 3 Yes 43. x x x 3(2 7) 1 4(3 1) 20, 2 − + = − + + = Yes 44. − + + = + + = − x x x 2(5 1) 3 7(4 7) 4, 3 No In Exercises 45–74, solve the equation. 45. − = x 7 11 18 46. − = y 4 13 17 47. + = y 7 9 2 48. + = x 9 4 −5 49. = − x 9 5 45 − 50. − = − x 7 8 56 51. x7 63 = − −9 52. − = x8 32 4− 53. = − − t 16 3 2 6− 54. = + x 25 4 5 5 55. − = − t t 6 8 4 2 3 56. − = + t t 6 7 8 9 −8 SECTION 6.1
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