# An Invitation to the Algebra of Canonical Commutation by Denes Petz

By Denes Petz

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Algebre Locale, Multiplicites. Cours au College de France, 1957 - 1958

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She takes a trip and drives an average of m miles each day for two weeks. Write an expression that represents the mileage on Sari’s odometer after her trip. (Lesson 1-1) Write a verbal expression for each algebraic expression. (Lesson 1-1) n 54. 5 + _ 55. q 2 - 12 2 x3 56. _ 9 PREREQUISITE SKILL Find the value of each expression. (pages 696–697, 700–701) 57. 075 58. 612 59. 425) 1 1 60. 4_ - 1_ 8 2 3 5 61. _ + 2_ 14 Chapter 1 The Language and Tools of Algebra 5 7 2 62. 8 ÷ _ 9 1-3 Open Sentences Main Ideas • Solve open sentence equations.

Which pair of values for x and y could José use to disprove Rachel’s theory? 25 D x = 6, y = 3 Read the Test Item The question is asking for a counterexample. Find the values of x and y that make the statement false. Solve the Test Item Replace x and y in the equation x ÷ y = 1 with the given values. 25 1 1=1✔ The hypothesis is true, and both values are whole numbers. The statement is true. 6 1 2≠1 Checking Results Since choice C is the correct answer, you can check your results by testing the other values.

4 - 3m)8 27. -3(2x - 6) Simplify each expression. If not possible, write simplified. 28. 2x + 9x 29. 4b - 1 + 5b 30. 5n 2 - 7n 31. 3a 2 + a + 14a 2 32. 12(4 + 3c) 33. (3x - 5)15 ANALYZE TABLES For Exercises 34 and 35, use the table that shows the monthly cost of a company health plan. Available Insurance Plans – Monthly Charges Coverage Medical Dental Vision Employee \$78 \$20 \$12 Family (additional charge) \$50 \$15 \$7 34. Write and evaluate an expression to calculate the total cost of medical, dental, and vision insurance for an employee for 6 months.