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Solving Equations

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  1. Solving Equations A “Balanced” Approach Skip to One-Step Equations Skip to Two-Step Equations Skip to Integer Practice

  2. Balance Basics • To keep the scale “balanced” the same amount of weight must be placed on both the left and right pan. • So if you add or remove items from one pan you must remove the same amount from the other pan to maintain balance.

  3. Solving Equations • The same method is used to solve equations: • Whatever is added, subtracted, multiplied or divided to one side the same must be done to the other side to keep the equation equal or “balanced”.

  4. For Example • Since both sides have the same value they are equal. • What happens if I take away 3 from the left pan? = 10 10

  5. Let’s Think About It • Are the left and right side values the same? • What could we do to make the right side the same as the left? = 10 - 3 10

  6. It Looks Like This • Correct: take 3 away from the right side. • What could we do to make the right side the same as the left? = 10 - 3 10 - 3

  7. Solving Equations • What is the value of the right side pan? • If the scale is balanced then what must the total value of the left side pan be? X + 3 7 • 7 is correct!

  8. Solving Equations • So if a number plus three is equal to 7 what is the missing number? X + 3 7

  9. Solving Equations • So if a number plus three is equal to 7 what is the missing number? • The missing number is 4 – Very Good 4 + 3 7

  10. Solving Equations • Write the missing number that will keep both the left and right side equal. Extra Practice Space

  11. Solving One-Step equations • Which side of the equation has the variable? • What is being done to the variable (+,-,×, ÷). • Do the opposite operation using the same number. • What you do to one side you must do to the other.

  12. Example 1

  13. Example 2

  14. Example 3

  15. Example 4

  16. Example 5

  17. Example 6 or Extra Practice Space

  18. Solving Two-Step equations • What is your variable • What is the furthest number from the variable on the same side. • How is the number attached? • Do the opposite. • What you do to one side you must do to the other. • Follow these steps until the variable is alone.

  19. Example 7

  20. Example 8 x= 5

  21. Example 9 -2 -2 Extra Practice Space x= 11

  22. Solve: x = -14 x = 1 x = 14 x = -1

  23. X = -14 2 Words of Advice 2 x= -14

  24. X = 14 -2 Words of Advice -2 x= 14

  25. X = 1 -2 Words of Advice -2 x= 1

  26. X = -1 2 2 Words of Advice x= -1

  27. Congratulations What shall we do next? Back to the beginning End Lesson

  28. Extra Practice for One-Step Equations 4m = 40 27 = 6 + b 12d = 144 a – 9 = 27 Extra Practice Space

  29. Extra Practice for Two-Step Equations 20 – x = 30 7p + 5 = 40 Extra Practice Space

  30. Extra Practice Space