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

Balance Basics To keep the scale “balanced” the same amount of weight must be placed on both the left and right pan. 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. 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: 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”. 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. Since both sides have the same value they are equal. What happens if I take away 3 from the left pan? What happens if I take away 3 from the left pan? 10 =

Let’s Think About It Are the left and right side values the same? Are the left and right side values the same? What could we do to make the right side the same as the left? What could we do to make the right side the same as the left? =

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

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

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

Solving Equations Write the missing number that will keep both the left and right side equal. Write the missing number that will keep both the left and right side equal. __ __ __ __ 15 Extra Practice Space

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

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6 or Extra Practice Space

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

Example 7

Example 8 x = 5

Example 9 -2 x = 11 Extra Practice Space

Solve: x = -14 x = 1 x = 14 x = -1 x = 14 x = -1

X = x = -14 Words of Advice

X = x = 14 Words of Advice

X = 1 -2 x = 1 Words of Advice

X = x = -1 Words of Advice

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

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

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