powerpoint presentation€¦ · ppt file · web view · 2012-01-08the 11th commandment (for...
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A Question of BalanceThe two sides on a balanced scale must be equal to each other
What does the Egg weigh?
E + 6 = 11E = 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
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
Multi-step equationsWhen and 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
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
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