1. Solving Algebraic Equations

2. Equality 3 = 3 3+4 = 3+4 3+4 = 7 For what value of x is: x + 4 = 7 true?

3. Equality 3 = 3 3+4 = 3+4 3+4 = 7 For what value of x is: x + 4 = 7 true? Answer: when x=3, then the equation is true.

4. How do I Solve Algebraic Equations? 1.What ever you add, subtract, multiply or divide to one side of the equation, you have to do the same to the other side of the equation! 2.Try to isolate the variable to one side of the equation. 3.Always substitute your answer for the variable to see if the answer and equation are true!

5. Example #1: x+4=7 x+4+(-4) = 7 + (-4) x + 0 = 3 x = 3 Substituting: 3 + 4 = 7 7 = 7 (CHECK!)

6. Example #2: 2x=4 2∙x 4 1∙x = 2 x = 2 2 2 = Substituting: 2x= 4 2∙2= 4 4 = 4 (CHECK!)

7. PROBLEMS: Solving Algebraic Equations Are you ready… 3,2,1… here we go!

8. Solve the Equation: v – 10 = -9

9. Answer: v - 10 +10 = -9+10 v + 0 = 1 v = 1

10. Solve the Equation: v – 10 = -3

11. Answer: v – 10 +10 = -3 +10 v + 0 = 7 v = 7

12. Solve the Equation: x – 3 = 4

13. Answer: x – 3 +3 = 4 +3 x + 0 = 7 x = 7

14. Note: x – 3 = 4 X = 4 + 3 X = 7

15. Getting back to Solving Equations… 3,2,1… here we go!

16. Solve the Equation: ― = 2 x5x5

17. Answer: (5)∙― = (5)∙2 1 ∙ x = 5∙2 x = 5∙2 (What do you notice?) x = 10 x5x5

18. Solve the Equation: 22 = -11k

19. Answer: = -2 = 1k -2 = k k = -2 22 -11 -11k -11

20. Solve the Equation: -13m = -377

21. Answer: m = 29

22. Solve the Equation: p + 8 = 14.1

23. Answer: p = 6.1

24. Solve the Equation: n + 4.7 = -4.7

25. Answer: n = -9.4

26. Solve the Equation: n + 3.9 = 0.7

27. Answer: n = -3.2

28. Solve the Equation: ― = -7 x 1.2

29. Answer: x = -8.4

30. Solve the Equation: -6.3k = -8.19

31. Answer: k = 1.3

32. Solve the Equation: 5½ + p = 6

33. Answer: p = ½

34. Solve the Equation: x – 3 = -5½

35. Answer: x = -2½

36. Solve the Equation: 9 ⅓ = ⁵⁄₃ ∙n

37. Answer: n = 5⅗

38. Solve the Equation: ―n = -1― 9 1 10 10

39. Answer: n = -1²⁄₉

40. Multiple Step Algebraic Equations

41. Solve the Equation: 1 – r = -5

42. Answer: r = 6

43. Solve the Equation: 3p – 2 = -29

44. Answer: p = -9

45. Solve the Equation: 4n - 9 = -9

46. Answer: n = 0

47. Solve the Equation: -5x + 13 = -17

48. Answer: x = 6

49. Solve the Equation: ― + 4 = 5 r 10

50. Answer: r = 10

51. Solve the Equation: ― + 5 = 3 n2n2

52. Answer: n = -4

53. Solve the Equation: = -7 k-10 2

54. Answer: k = -4

55. Solve the Equation: = 2 9+m 3

56. Answer: m = -3

57. Solve the Equation: = -1 -5+x 22

58. Answer: x = -17

59. Solve the Equation: -5 + ― = 0 n3n3

60. Answer: n = 15

61. Solve the Equation: ― + 8 = 7 p4p4

62. Answer: p = -4

63. Solve the Equation: ― - 5 = -8 y -4

64. Answer: y = 12

65. Solve the Equation: 0.4x + 3.9 = 5.78

66. Answer: x = 4.7

67. Solve the Equation: 9.2r + 5.514 = 158.234

68. Answer: r = 16.6

69. Solve the Equation: ― - 4.9 = -7.11 m 2.8

70. Answer: m = -6.188

71. Solve the Equation: + = X2X2 3535 4545

72. Answer: x = ⅖

73. Solve the Equation: x + 1 = 2 3232 1313 2323

74. Answer: x = ⁸⁄₉