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By doing the opposite, we keep the sides of the equation balanced .

SOLVING EQUATIONS • The single most important skill in algebra • Goal: Find the one value of the variable that makes the sentence true. For instance, if 2x + 3 = 17, then 7 is the only value of x that will make this a true sentence. So x = 7.

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By doing the opposite, we keep the sides of the equation balanced .

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  1. SOLVING EQUATIONS• The single most important skill in algebra• Goal: Find the one value of the variable that makes the sentence true.

  2. For instance, if 2x + 3 = 17,then 7 is the only value of x that will make this a true sentence.So x = 7.

  3. • We can solve equations by doing the OPPOSITE of what has been done to the variable in the problem.• If a problem says +, you subtract.• If a problem has multiplication, you divide.

  4. By doing the opposite, we keep the sides of the equation balanced.

  5. As long as you do the SAME thing to both sides of an equation, it will remain balanced.

  6. 7x – 13 = 50

  7. 7x – 13 = 50 +13 +137x = 63

  8. 7x – 13 = 50 +13 +137x = 63 7 7 x = 9

  9. -5x + 7 = 82

  10. -5x + 7 = 82 - 7 - 7-5x = 75

  11. -5x + 7 = 82 - 7 - 7-5x = 75-5 -5 x = -15

  12. 4x + 25 = 13

  13. 4x + 25 = 13- 25 -254x = -12

  14. 4x + 25 = 13 - 25 -254x = -12 4 4 x = -3

  15. When you solve equations, you also do the opposite of the order of operations. Add/subtract firstThen divide/multiply

  16. Solve these equations:4a+ 11 = 59-2b + 13 = 55c – 72 = 98-4d + 11 = 47

  17. Solve these equations:4a+ 11 = 59  a = 12-2b + 13 = 5  b = 45c – 72 = 98  c = 34-4d + 11 = 47  d = -9

  18. Solve these equations:5x – 18 = 402y + 73 = 54-3z + 5 = 1

  19. Solve these equations:5x – 18 = 40 x = 58/5 or 11.62y + 73 = 54 y = -19/2 or -9.5 _-3z + 5 = 1 z = 4/3 or 1.3

  20. Some equations are even easier.n + 4 = 135x = 35

  21. Some equations are even easier.n + 4 = 13Just subtract 4 … x = 95x = 35Just divide by 5 … x = 7

  22. Solve 17 = 3x – 7

  23. Solve 17 = 3x – 7+7 +724 = 3x

  24. Solve 17 = 3x – 7+7 +724 = 3x 3 3 8 = x

  25. Solve 19 – 2x = 104

  26. Solve 19 – 2x = 104-19 -19 -2x = 85

  27. Solve 19 – 2x = 104-19 -19-2x = 85 -2 -2 x = -85/2 or -42.5

  28. If you know the basic steps, you can quickly do equations with more difficult numbers using a calculator.

  29. 12x + 1794 = 2127

  30. 12x + 1794 = 2127

  31. 963 – 25x = 704

  32. 963 – 25x = 704

  33. What about this?

  34. Fractions mean division, so to cancel, we’ll subtract 13 and then multiply by 7. n = 63

  35. Things that can complicate solving equations …

  36. Parentheses• Use distributive property first.Like terms• Combine them first.

  37. 3(2x – 5) = 27

  38. 3(2x – 5) = 27

  39. 3(2x – 5) = 27 6x – 15 = 27 6x = 42 x = 7

  40. -7(2x – 11) = 98

  41. -7(2x – 11) = 98 -14x + 77 = 98 -14x = 21 x = -3/2 or -1.5

  42. 4p + 3 – 2p + 7 + 5p + 2 = 17

  43. 4p + 3– 2p+ 7+5p+ 2 = 177p + 12 = 17 7p = 5 p = 5/7

  44. 5(3x + 5) – 3(2x – 1) = 145

  45. 5(3x + 5) – 3(2x – 1) = 145 15x + 25 – 6x + 3 = 145

  46. 5(3x + 5) – 3(2x – 1) = 14515x + 25– 6x + 3 = 1459x + 28 = 145

  47. 5(3x + 5) – 3(2x – 1) = 145 15x + 25 – 6x + 3 = 145 9x + 28 = 145 9x = 117 x = 13

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