Solving EquationsSolving EquationsA “Balanced” ApproachA “Balanced” Approach

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Balance BasicsBalance Basics

To keep the scale To keep the scale “balanced” the same “balanced” the same amount of weight must amount of weight must be placed on both the be placed on both the left and right pan.left and right pan.

So if you add or remove So if you add or remove items from one pan you items from one pan you must remove the same must remove the same amount from the other amount from the other pan to maintain pan to maintain balance.balance.

Solving EquationsSolving Equations

The same method The same method is used to solve is used to solve equations:equations: Whatever is added, Whatever is added,

subtracted, subtracted, multiplied or divided multiplied or divided to one side the to one side the same must be done same must be done to the other side to to the other side to keep the equation keep the equation equal or “balanced”.equal or “balanced”.

For ExampleFor Example

Since both sides Since both sides have the same have the same value they are value they are equal.equal.

What happens if I What happens if I take away 3 from take away 3 from the left pan?the left pan? 10 10=

Let’s Think About ItLet’s Think About It

Are the left and Are the left and right side values right side values the same?the same?

What could we do What could we do to make the right to make the right side the same as side the same as the left?the left? 10 -

310=

It Looks Like ThisIt Looks Like This

Correct: take 3 Correct: take 3 away from the away from the right side.right side.

What could we do What could we do to make the right to make the right side the same as side the same as the left?the left? 10 -

3= 10 -

3

Solving EquationsSolving Equations

What is the value of What is the value of the right side pan?the right side pan?

If the scale is If the scale is balanced then what balanced then what must the total value must the total value of the left side pan of the left side pan be?be?

X + 3 7

7 is 7 is correct!correct!

Solving EquationsSolving Equations

So if a number plus So if a number plus three is equal to 7 three is equal to 7 what is the missing what is the missing number?number?

X + 3 7

Solving EquationsSolving Equations

So if a number plus So if a number plus three is equal to 7 three is equal to 7 what is the missing what is the missing number?number?

The missing The missing number is 4 – Very number is 4 – Very GoodGood

74 + 3

Solving EquationsSolving Equations

Write the missing Write the missing number that will number that will keep both the left keep both the left and right side and right side equal.equal.

__ + 3__ + 3 77

__ - 4__ - 4 1010

10 - __10 - __ 66

4 + __4 + __ 1515

Extra Practic

e Space

Solving One-Step equationsSolving One-Step equationsA.A. Which side of the equation has the variable?Which side of the equation has the variable?

B.B. What is being done to the variable (What is being done to the variable (+,-,×, ÷)+,-,×, ÷)..

C.C. Do the opposite operation using the same number.Do the opposite operation using the same number.

D.D. What you do to one side you must do to the other.What you do to one side you must do to the other.

Example 1Example 1

8 7x 8 8

15x

Example 2Example 2

8 16x 8 8

15x

Example 3Example 3

3 7x 8 8

15x

Example 4Example 4

3 15x 3 3 5x

3 15x

5x

1 13 15

3 3x

Example 5Example 5

7 35x 3 3 5x

7 35x 5x

7 35x

Example 6Example 6

26

3x

x

26

3x

orExtra Practic

e Space

Solving Two-Step equationsSolving Two-Step equationsA.A. What is your variableWhat is your variable

B.B. What is the furthest number from the variable on What is the furthest number from the variable on the same side.the same side.

C.C. How is the number attached?How is the number attached?

D.D. Do the opposite.Do the opposite.

E.E. What you do to one side you must do to the other.What you do to one side you must do to the other.

F.F. Follow these steps until the variable is alone.Follow these steps until the variable is alone.

Example 7Example 7

10194

3

c

3 14 10c 14 14

3 24c

8c 3 3

Example 8Example 8

783 x88 15- 3 x

3 3 x = 5

Example 9Example 9

10212 x1212222 x

-2 -2

x = 11Extra

Practice

Space

Solve:Solve: 2 13 15x

x = x = -14-14 x = x = 1 1

x = x = 14 14 x = x = -1-1

X X = -14= -14

2 13 15x 1313

2 28x

2 2

x = -14

Words of

Advice

X X = 14= 14

2 13 15x 1313

2 28x

-2 -2

x = 14

Words of

Advice

X X = 1= 1

2 13 15x 1313

2 2x

-2 -2

x = 1

Words of

Advice

X X = -1= -1

2 13 15x 1313

2 2x 2 2

x = -1Words

of Advice

CongratulationsCongratulations

What shall we do next?What shall we do next?

Back to the beginning

End Lesson

Extra Practice for One-Step Extra Practice for One-Step EquationsEquations

4m = 40

12d = 144a – 9 = 27

27 = 6 + b

Extra Practic

e Space

Extra Practice for Two-Step Extra Practice for Two-Step EquationsEquations

7p + 5 = 40 20 – x = 30

Extra Practic

e Space

Extra Practice SpaceExtra Practice Space