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Solving One and Two step Equations

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  1. Solving One and Two step Equations Sol A.1

  2. Why do we do the same thing to both sides of an equation d + 12 = -5

  3. Why do we do the same thing to both sides of an equation • https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/why-of-algebra/v/why-we-do-the-same--thing-to-both-sides--simple-equations

  4. r + 16 = -7 Ex. 1) Solve r + 16 = -7 Think of this equation as a balance scale. Whatever you do to one side has to be done to the other to keep it balanced!

  5. 1) Solve r + 16 = -7

  6. 1) Solve r + 16 = -7 • Draw “the river” to separate the equation into 2 sides • Subtract 16 from both sides • Simplify vertically • Check your answer by substituting your answer back into the problem - 16 -16 r = -23 -23 + 16 = -7

  7. Ex. 2) Solve x + 2 = -3

  8. 2) Solve x + 2 = -3 - 2 - 2 x = -5 -5 + 2 = -3 • Draw “the river” to separate the equation into 2 sides • Subtract 2 from both sides • Simplify vertically • Check your answer by substituting your answer back into the problem On homework and tests, be sure to check your work!! There is no reason why you should miss a problem!

  9. Addition and subtraction Properties of Equality • Definition: Either adding or subtracting the same number to each side of the equation produces an equivalent equation. Example: X - 9 = 15 How can you check your answers?

  10. Try These: Don’t forget to check your answer 3. r – 2 = 21 4. m + 17 = 3 5. b – (-4) = 9

  11. 3. r – 2 = 21

  12. 4. m + 17 = 3

  13. 5. b – (-4) = 9

  14. Multiplication and Division Properties of Equality Definition: If you multiply or divide each side of the equation by the same nonzero number you produce an equivalent equation. Example 6: Multiplication:

  15. Division: Example 7. 7m=91

  16. Try These: 8. -6m = 48 9. 14 = -x 10.

  17. -6m = 48

  18. 14 = -x

  19. 10.

  20. Solving Equations using Reciprocals Rule – When the original number is multiplied by it’s reciprocal the product should equal 1. Example 11: Don’t forget to check your answer

  21. Example 12

  22. Solving Two Step Equations Note- When solving two step equations Always Isolate the variable first. (i.e. get rid of anything that is not with your variable.) Example 13:

  23. Solving Two Step Equations Example 14:

  24. Try These: 15. 16. 17.

  25. 15.

  26. 16.

  27. 17.

  28. Solving Two-Step equations by combining like terms Example: 18. 7x – 4x = 21 19. 5b – 7b = 4