Equations-Sec 1

1
Solving Equations
Involving One Operation
2
A Question of Balance
The two sides on a balanced scale must be equal
to each other
E 6 11
E 5
What does the Egg weigh?
3
A Question of Balance
The two sides of an equation are equal to each
other
The left side and the right side must be balanced
2(3) 4
10
When you do something to one side of an equation,
You have to do the same thing to the other side.
4
A Question of Balance
If the two sides of an equation are not equal
3(7) 2
20 1
5
A Question of Balance
If the two sides of an equation are not equal
Then it is not balanced!
3(7) 2
20 1
6
A Question of Balance
What happens if we change one of the sides of a
balanced equation?
8 3
1
8 3 1
11
Then it is not balanced!
7
A Question of Balance
What happens if we change one of the sides of a
balanced equation?
11
1
8 3 1
We need to make the same change to the other side!
Then it is not balanced!
8
A Question of Balance
What happens if we change one of the sides of a
balanced equation?
8 3 1
11 1
The 11th Commandment (for equations)
We need to make the same change to the other side!
We need to make the same
change to the other side!
Whatever thou dost unto the left, thou also must
do unto the right.
9
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!
10
In the equation,
7 added to a number gives 15 Solving the
equation means, finding the value of the variable
that makes the equation true.
Lets go back to the balance
11
The 11th Commandment (for equations)
Whatever thou dost unto the left, thou also must
do unto the right.
x 7
- 7
15
- 7
Subtract 7 from both sides
Simplify both sides
12
The 11th Commandment (for equations)
Whatever thou dost unto the left, thou also must
do unto the right.
Subtract 7 from both sides
Simplify both sides
Now we know the value of x
13
The 11th Commandment (for equations)
Whatever thou dost unto the left, thou also must
do unto the right.
So the solution goes like this
x 7 15
x 7 7 15 7
Subtract 7 from both sides
Simplify both sides
x 8
Now we know the value of x
14
In some equations, the solution is obvious.
x 7 12
5n 35
x 19
n 7
20 h 41
h 21
c 24
We can simply work the operation backwards in our
head to get the answer.
15
But in other equations, the solution is not so
obvious.
We have to know what operation(s) must be done to
solve it, and work it out carefully.
16
But in other equations, the solution is not so
obvious.
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 multiplication is division
17
Multi-step equations

• When 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.

18
How would we solve 3x 5 12? Lets take
another look at the balance
3x 5
12
5
5
Subtract 5 from both sides
19
How would we solve 3x 5 12? Lets take
another look at the balance
3x
7
Subtract 5 from both sides
Simplify
20
How would we solve 3x 5 12? Lets take
another look at the balance
7
3x
3
3
Subtract 5 from both sides
Simplify
Divide both sides by coefficient of the variable
(3)
21
How would we solve 3x 5 12? Lets take
another look at the balance
7
x
3
Subtract 5 from both sides
Simplify
Divide both sides by coefficient of the variable
(3)
22
Lets try some more equations Remember, we have
to keep the equations balanced!
Solve
8m 10 36
8m 10 10 36 10
8m 46
8 8
m
w 84
23
Notice that there are variables on both sides
5x ? 2 x 4
Solve
Get rid of the -2 on the left side
5x ? 2 2 x 4 2
5x x 6
Simplify
Get rid of the x on the right side
5x x x x 6
4x 6
Simplify
Get rid of the cofficient of x
4 4
Simplify
x