A Question of BalanceThe two sides on a balanced scale must be equal to each other

What does the Egg weigh?

E + 6 = 11

E = 5

When you do something to one side of an equation,You have to do the same thing to the other side.

A Question of Balance

2(3) + 4 10

The two sides of an equation are equal to each otherThe left side and the right side must be balanced

A Question of BalanceIf the two sides of an equation are not equal…

3(7) – 2 20 + 1

A Question of BalanceIf the two sides of an equation are not equal…

3(7) – 220 + 1

Then it is not balanced!

A Question of BalanceWhat happens if we change one of the sides of a

balanced equation?

Then it is not balanced!

8 + 3

11+ 18 + 3 + 1

A Question of BalanceWhat happens if we change one of the sides of a

balanced equation?

Then it is not balanced!

8 + 3 + 1

11

We need to make the same change to the other side!

+ 1

We need to make the same change to the other side!

What happens if we change one of the sides of a balanced equation?

A Question of Balance

8 + 3 + 1

11 + 1

We need to make the same change to the other side!Whatever thou dost unto the left, thou also must do unto the right.

The 11th Commandment (for equations):

To solve an equation means to find every number that makes the equation true.

We do this by adding or subtracting to each side of the

equation … but always keep it balanced!

In the equation, 157 x7 added to a number gives 15…

Solving the equation means, finding the value of the variable that makes the equation true.

Let’s go back to the balance

Example: 1

x + 7 15

Whatever thou dost unto the left, thou also must do unto the right.

The 11th Commandment (for equations):

- 7 - 7

Subtract 7 from both sidesSimplify both sides

Whatever thou dost unto the left, thou also must do unto the right.

The 11th Commandment (for equations):

x 8

Subtract 7 from both sidesSimplify both sidesNow we know the value of x

x 8

Subtract 7 from both sides Simplify both sidesNow we know the value of x

Whatever thou dost unto the left, thou also must do unto the right.

The 11th Commandment (for equations):

So the solution goes like this…x + 7 = 15x + 7 – 7 = 15 – 7

x = 8

In some equations, the solution is obvious.x – 7 = 12

x = 19 5n = 35

n = 7

20 + h = 41h = 21

8c

= 3

c = 24We can simply work the operation

backwards in our head to get the answer.

But in other equations, the solution is not so obvious.

93127 x 08.12.3 w

43

52

p

We have to know what operation(s) must be done to solve it, and work it out carefully.

452.1 m

But in other equations, the solution is not so obvious. 93-127 x 08.12.3 w

43

52

p 452.1 m

12793-127127 x220-x

2.308.12.32.3 w28.4w

43

25

52

25

p

815

p

2.145

2.12.1

m

75.3m

You have to do the inverse operation to both sides to get the variable by itself

The opposite of addition is subtraction

The opposite of subtraction is addition

The opposite of

multiplying by

is multiplying by52

25

The opposite of multiplication is division

Ex2. Ex3.

Ex4.Ex5.

Multi-step equationsWhen an equation has more than one operation you still have to isolate the variable by doing the following:•Make sure variable terms are all on one side, and constant terms are on the other.•Simplify•Divide by the coefficient of the variable.

3x + 5 12

How would we solve 3x + 5 = 12?Let’s take another look at the balance

– 5 – 5

Subtract 5 from both sides

Ex.6

3x 7

How would we solve 3x + 5 = 12?Let’s take another look at the balance

Subtract 5 from both sidesSimplify

3x 7

How would we solve 3x + 5 = 12?Let’s take another look at the balance

Subtract 5 from both sidesSimplify

33

Divide both sides by coefficient of the variable (3)

7

How would we solve 3x + 5 = 12?Let’s take another look at the balance

Subtract 5 from both sidesSimplify

3x

Divide both sides by coefficient of the variable (3)

So the solution is: 37x

Let’s try some more equationsRemember, we have to keep the equations balanced!

Solve:8m – 10 = 36

423

31176w

173117176w 8m – 10 + 10 = 36 + 10

8m = 468 8m =

146w

1466w6

w = 84

Ex7. Ex8.

5x 2 = x + 4 Solve:

5x 2 + 2 = x + 4 + 2

Notice that there are variables on both sides

5x = x + 6

Get rid of the -2 on the left side

Simplify

5x – x = x – x + 6 Get rid of the x on the right side

4x = 6 Get rid of the cofficient of x4 4

23x = Simplify

Simplify

Ex9.