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## Solving Equations

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**Solving Equations**A “Balanced” Approach Skip to One-Step Equations Skip to Two-Step Equations Skip to Integer Practice**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.**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”.**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**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**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**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!**Solving Equations**• So if a number plus three is equal to 7 what is the missing number? X + 3 7**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**Solving Equations**• Write the missing number that will keep both the left and right side equal. Extra Practice Space**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.**Example 6**or Extra Practice Space**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.**Example 8**x= 5**Example 9**-2 -2 Extra Practice Space x= 11**Solve:**x = -14 x = 1 x = 14 x = -1**X = -14**2 Words of Advice 2 x= -14**X = 14**-2 Words of Advice -2 x= 14**X = 1**-2 Words of Advice -2 x= 1**X = -1**2 2 Words of Advice x= -1**Congratulations**What shall we do next? Back to the beginning End Lesson**Extra Practice for One-Step Equations**4m = 40 27 = 6 + b 12d = 144 a – 9 = 27 Extra Practice Space**Extra Practice for Two-Step Equations**20 – x = 30 7p + 5 = 40 Extra Practice Space