1. Involving One Operation
Solving Equations
Involving One Operation

2. The two sides on a balanced scale must be equal to each other
A Question of Balance
The two sides on a balanced scale must be equal to each other
E =
E =
What does the Egg weigh?

3. The left side and the right side must be balanced
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. If the two sides of an equation are not equal…
A Question of Balance
If the two sides of an equation are not equal…
3(7) – 2
20 + 1

5. If the two sides of an equation are not equal…
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. What happens if we change one of the sides of a balanced equation?
A Question of Balance
What happens if we change one of the sides of a balanced equation?
8 + 3
+ 1 11
Then it is not balanced!

7. We need to make the same change to the other side!
A Question of Balance
What happens if we change one of the sides of a balanced equation? 11
+ 1
Then it is not balanced!
We need to make the same change to the other side!

8. A Question of Balance 8 + 3 + 1 11 + 1
What happens if we change one of the sides of a balanced equation?
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. Let’s go back to the balance
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.
Let’s go back to the balance

11. x + 7 - 7 15 - 7 Simplify both sides Subtract 7 from both sides
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. x 8 Subtract 7 from both sides Simplify both sides
The 11th Commandment (for equations):
Whatever thou dost unto the left, thou also must do unto the right. x 8
Subtract 7 from both sides
Now we know the value of x
Simplify both sides

13. The 11th Commandment (for equations):
Whatever thou dost unto the left, thou also must do unto the right. x 8
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
= 3
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
But in other equations, the solution is not so obvious.
The opposite of addition is subtraction
The opposite of subtraction is addition
The opposite of multiplying by is multiplying by
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?
Let’s take another look at the balance
3x + 5
– 5 12
– 5
Subtract 5 from both sides

19. How would we solve 3x + 5 = 12?
Let’s take another look at the balance 3x 7
Subtract 5 from both sides
Simplify

20. Divide both sides by coefficient of the variable (3)
How would we solve 3x + 5 = 12?
Let’s take another look at the balance 3x 7 3 3
Subtract 5 from both sides
Simplify
Divide both sides by coefficient of the variable (3)

21. Divide both sides by coefficient of the variable (3)
How would we solve 3x + 5 = 12?
Let’s take another look at the balance 7 x 3
Subtract 5 from both sides
Simplify
So the solution is:
Divide both sides by coefficient of the variable (3)

22. Let’s try some more equations
Remember, we have to keep the equations balanced!
Solve:
8m – 10 = 36
8m – =
8m = 46
m =
w = 84

23. 5x  2 = x + 4 5x  2 + 2 = x + 4 + 2 5x = x + 6 5x – x = x – x + 6
Notice that there are variables on both sides
Solve:
5x  2 = x + 4
5x  = x
Get rid of the -2 on the left side
5x = x + 6
Simplify
5x – x = x – x + 6
Get rid of the x on the right side
4x = 6
Simplify
Get rid of the cofficient of x
x =
Simplify