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