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Solving Algebraic Equations

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  1. Solving Algebraic Equations

  2. Equality3 = 33+4 = 3+43+4 = 7For what value of x is: x + 4 = 7 true?

  3. Equality3 = 33+4 = 3+43+4 = 7For 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? 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! Try to isolate the variable to one side of the equation. 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+10v + 0 = 1v = 1

  10. Solve the Equation: v – 10 = -3

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

  12. Solve the Equation: x – 3 = 4

  13. Answer:x – 3 +3 = 4 +3x + 0 = 7x = 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 x 5

  17. Answer:(5)∙― = (5)∙21 ∙ x = 5∙2x = 5∙2(What do you notice?)x = 10 x5

  18. Solve the Equation: 22 = -11k

  19. Answer:=-2 = 1k-2 = kk = -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: 9⅓ = ⁵⁄₃ ∙n

  37. Answer:n = 5⅗

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

  39. Answer:n = -1²⁄₉

  40. Word Problems

  41. Solve the word problem: A number increased by 34 is 134.

  42. Answer:n + 34 = 134n = 100

  43. Solve the word problem: Find the number Seventy-five less than a number is 62.

  44. Answer:n - 75 = 62n = 137

  45. Solve the word problem: A number increased by 14 is 49.

  46. Answer:n + 14 = 49n = 35

  47. Solve the word problem: Find the number Twenty-nine more than a number is 52.

  48. Answer:n + 29 = 52n = 23

  49. Solve the word problem: Find the number One-half of a number is 9.

  50. Answer:½(n)= 9n = 18