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Name _____________________ Class & Block ______________ Date ______________________ Write an algebraic expression to represent each verbal expression. 1. ____________ seven more than the product of a number and 10 2. ____________ four less than the square of a number 3. ____________ the product of the cube of a number and -6 4. ____________ five times the sum of 9 and a number 5. ____________ twice the sum of a number and 8 6. ____________ the square of the quotient of a number and 4 7. ____________ the cube of the difference of a number and 7 Write a verbal expression to represent each equation. 8. x – 5 = 12 9. 3a2 = a + 4 10. b = 2(b + 1) Write an inequality for each problem. Then solve. (Don’t graph) 11. ___________ Twenty less than a number is more than twice the same number. 12. ____________ Four times the sum of twice a number and -3 is less than 5.5 times that same number. 13. ____________ Nineteen more than a number is less than 42. 14. ____________ The difference of three times a number and 16 is at least 8. 15. ____________ One half of a number is more than 6 less than the same number. 16. ____________ Five less than the product of 6 and a number is no more than twice that same number. Name _____________________ Class & Block ______________ Date ______________________ Write an absolute value inequality for each of the following. (Sketch a graph if needed.) 17. ____________ all numbers greater than or equal to 5 or less than or equal to -5 18. ____________ all numbers less than 7 and greater than -7 19. ____________ all numbers between -4 and 4 20. ____________ all numbers less than or equal -6 and greater than or equal to 6 Name the property illustrated in each statement. 21. 67 + 3 = 3 + 67 ___________________ 32. gx = xg __________________ 22. (2a + 3b) + 4c = 2a + (3b + 4c) 33. g(5*h) = (g*5)h __________________ ___________________ 23. 4(a + 5b) = 4a + 20b 34. 6u + 12v = 6(u + 2v) __________________ ___________________ 35. 8 * 1 = 8 __________________ 24. (2 + 3)a + 7 = 5a + 7 36. 3 + (-3) = 0 ___________________ 25. k + 0 = k ___________________ __________________ 37. x + y = y + x __________________ 26. 5 * (1/5) = 1 ___________________ 38. 8 + (3 + 9) = 8 + 12 27. If 3 + 5 = 6 + 2, then 6 + 2 = 3 + 5 __________________ ___________________ 39. 3 + 0 = 3 28. fh + 2g = hf + 2g __________________ ___________________ 40. (3/x)(x/3) = 1 29. 5(m*n) = (5*m)n __________________ ___________________ 41. (5x2 + x + 3)+15=(5x2 + x)+(3 + 15) 30. 1 * b2 = b2 ____________________ 31. 4(0) = 0 __________________ 42. a + (-a) = 0 ____________________ __________________ Name _____________________ Class & Block ______________ Date ______________________ 43. If 7 * 2 = 14, then 14 = 7 * 2 45. If 2x = 3d and 3d = -4, then 2x = -4 ____________________ 44. If ab = 0, then a = 0 and/or b = 0 _____________________ 46. m + (-8) = m + (-8) ___________________ _____________________ 47. Explain the property demonstrated in each step: a. 3c + 5(2 +c) = 3c + 5(2) + 5c ___________________ = 3c + 5c + 5(2) ___________________ = (3c + 5c) + 5(2) ___________________ = (3 + 5)c + 5(2) ___________________ = 8c + 10 ___________________ 48. Chemists use water to dilute acid. One important rule of chemistry is to always pour the acid into the water. Pouring water into acid could produce spattering and burns. a. Would you say that combining acid and water is commutative? __________________ b. Give an example from your life that is commutative. __________________________ c. Give an example from your life that is not commutative. ________________________ Name _____________________ Class & Block ______________ Date ______________________