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 __ + 3 7 __ - 4 10 10 - __ 6 4 + __ 15 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 1 This step is called the Addition Property of Equality.

Example 2 This step is called the Subtraction Property of Equality.

Example 3 What property is this? Addition Property of Equality

x = -2 Example 4 x + 6 = 4 – 6 – 6 What property is this? – 6 – 6 Subtraction Property of Equality x = -2

x = 3 Example 5 x – 2 = 1 + 2 + 2 What property is this? + 2 + 2 Addition Property of Equality x = 3

y = 6 Example 6 14 + y = 20 – 14 – 14 What property is this? – 14 – 14 Subtraction Property of Equality y = 6

z = 20 Example 7 12 = z – 8 +8 + 8 What property is this? +8 + 8 Addition Property of Equality z = 20

y = 7 Example 8 y – 3 = 4 +3 + 3 What property is this? +3 + 3 Addition Property of Equality y = 7

y = 3 Example 9 y + 6 = 9 – 6 – 6 What property is this? – 6 – 6 Subtraction Property of Equality y = 3

q = -1 Example 10 q – 8 = -9 + 8 + 8 What property is this? + 8 + 8 Addition Property of Equality q = -1

Example 11 An angelfish can grow to be 12 inches longs. If an angelfish is 8.5 inches longer than a clown fish, how long is a clown fish? 12 = c + 8.5 3.5 = c

One Step Equation Multiplication and Division

Example 1

Example 2

Example 3 or Extra Practice Space

Example 4  

Example 5  

Example 6  

Example 7  

Example 8  

Lelah sent 574 text messages last week Lelah sent 574 text messages last week. On average, how many messages did she send each day?

 

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 7

Example 8 x = 5

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

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

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

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

X = 1 Words of Advice -2 -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 Extra Practice Space

Extra Practice Space