1. Solving Equations (Addition & Subtraction)
Grade Seven & Eight Mathematics
M. M. Couturier

2. Solving Algebraic Expressions
Algebra is a lot like a store: everything evens out. If a person takes $45.00 worth of products, the person gives $45.00 to the store clerk. In algebra, what happens to one side of the equal sign, must happen to the other. In this unit, you may wish to have a pen or crayon of a different colour in order to do your work.

3. Solving Algebraic Expressions
Example: Let’s take an algebraic expression and solve it:
x + 10 = 20
The first key in solving an algebraic expression is to ISOLATE the unknown variable, in this case “x”. To do so, we must get rid of the 10. How?

4. Solving Algebraic Expressions
If we were to take away 10 from the left side, we would then have to take away ten from the right side. Since taking away means subtraction, we will:
x + 10 – 10 =
What you do to one side, you must do to the other. Notice that the 10’s on the left are going to disappear, since (10-10 = 0).

5. Solving Algebraic Expressions
Hence:
x + 10 – 10 =
x = 10

6. Solving Algebraic Expressions
Let’s do another:
y + 3 = 20
Again, we want to ISOLATE the unknown variable (y), so we must get rid of the 3.
y + 3 – 3 =
Recall that what you do to one side, you must do to the other. Hence,
y = 17

7. Solving Algebraic Expressions
Let’s do another:
z + 5 = 3
Again, we want to ISOLATE the unknown variable (z), so we must get rid of the 5.
z + 5 – 5 = 3 - 5
Recall that what you do to one side, you must do to the other. Hence,
z = -2

8. Solving Algebraic Expressions
One more for good luck:
3 + f = 19
Again, we want to ISOLATE the unknown variable (f), so we must get rid of the 3.
3 – 3 + f =
Recall that what you do to one side, you must do to the other. Hence,
f = 16

9. Solving Algebraic Expressions
What do we do in the event of subtraction?
d - 6 = 54
Again, we want to ISOLATE the unknown variable (d), so we must get rid of the (-6). Remember thought, we are trying to get rid of the number, we will therefore have to add 6. Think about it now!!!
d – =

10. Solving Algebraic Expressions
Take extra careful note:
= 0
- 6 – 6 = -12
6 – 6 = 0
6 + 6 = 12

11. Solving Algebraic Expressions
Hence, we add 6 in this case, to get:
d – =
Still keeping in mind that what you do to one side, you must do to the other.
d = 60

12. Solving Algebraic Expressions
Let’s do another:
z - 5 = 3
Again, we want to ISOLATE the unknown variable (z), so we must get rid of the 5.
z = 3 + 5
Recall that what you do to one side, you must do to the other. Hence,
z = 8

13. Solving Algebraic Expressions
Let’s do another:
y - 3 = 20
Again, we want to ISOLATE the unknown variable (y), so we must get rid of the 3.
y =
Recall that what you do to one side, you must do to the other. Hence,
y = 23

14. Solving Algebraic Expressions
Let’s do another:
t – 12 = -20
Again, we want to ISOLATE the unknown variable (t), so we must get rid of the (-12).
t =
Recall that what you do to one side, you must do to the other. Hence,
y = -8