1. EQUATIONS FOR HIGHER LEVELS
At this level to solve equations we use a few simple rules but also must remember that solutions can be negative and also may not be a whole number.
Change the sides, Changes the sign

2. TWO STAGE EQUATIONS Examples: 1. 4y – 8 = 7 4y = 7 + 8 4y = 15 y =
Divide by 4 to find y
You can leave the answer as a fraction.
y = 3.75

3. 2. 6r = - 10
6r = - 10 – 5
6r = - 15
r =
r = - 2.5

4. EQUATIONS WITH TWO UNKNOWNS
Equations that contain two unknown values on different sides of the equals sign need to be COLLECTED together on the same side.
Number terms should also be collected together on the opposite side.

5. Examples:
s - 8 = 4s + 3
7s - 4s =
3s = 11
s =
s = 3.66
11a + 7 = 5a + 4
11a - 5a =
6a = - 3
a =
a = - 0.5

6. EQUATIONS THAT CONTAIN BRACKETS
Before solving any equation that contains brackets we must remove the brackets first.
Removing Brackets
Multiply the terms inside the bracket by the term outside.
5(4d + 3) = 20d + 15
Do not forget the second term in the bracket.
- 7 (5x - 2) =
- 35x + 14
Note: (-) x (-) = (+)

7. Examples:
3(2x - 8) = Remove bracket
6x – 24 = 3
6x =
6x = 27
x =
x = 4.5

8. 2. 3(2x + 1) = 4x - 9 Remove bracket
6x = 4x Collect x's together
6x - 4x =
2x = - 12
x = - 6

9. 3. 4x + 6x – = 7x + 28
10x = 7x + 28
10x – 7x =
3x = 40
x =
x =

10. EQUATIONS WITH FRACTIONS
Equations that contain fractions are solved in the same manner.
When changing sides we must remember that a divide becomes a multiply and vice versa.