Solving
an Equation with Two or More Unknown Terms:
When the equation has two or more terms indicating an unknown number,
then the first step is to simplify it by combining the like terms
and use either the appropriate axiom or transposition method to
solve the equation.
Example
1: Solve: 9
– 8 – 3
= 4
| |
|
Solution |
| |
|
9
– 8 – 3
= 4 |
Collect
like terms |
|
9
– 3
– 8 = 4 |
Combine
like terms
|
|
6
– 8 = 4 |
Transpose
– 8 to the right side of the equation
|
|
6
= 4 + 8 |
Add
right side terms
|
|
6
= 12 |
Find
the value for (divide)
|
|
=
12 ÷ 6 |
Answer
|
|
=
2
|
| Check:
9
– 8 – 3
= 4 |
|
| |
(9
× 2) – 8 – (3 × 2) = 4
18 – 8 –
6 = 4
18 – 14 = 4
4 = 4
|
|
Example
2: Solve:
8 + 7b – 2 – 5b = 12
| |
|
Solution |
|
|
| |
|
8
+ 7b – 2 – 5b = 12 |
|
Collect
like terms
|
|
7b
– 5b + 8
– 2 = 12 |
|
Combine
like terms |
|
2b
+ 6 = 12 |
|
Use
the axiom 1
to cancel the term 6
(add - 6 to both sides of the equation) |
|
2b
+ 6 – 6 = 12 – 6 |
|
|
Subtract
|
|
2b
+ 0 = 6 |
|
|
Find
the value for b (divide)
|
|
b
= 6 ÷ 2 |
|
|
Answer
|
|
b
= 6 ÷ 2 |
|
|
|
|
|
|
|
Axiom 1: The same number can
be subtracted from each side of an equation without altering the
equality of the equation.
| Check: |
8
+ 7b – 2 – 5b = 12 |
|
|
| |
8
+ (7 × 3) – 2 – (5 × 3) = 12
|
|
| |
8
+ 21 – 2 – 15 = 12
|
|
|
| |
29
– 17 = 12 |
|
|
| |
12
= 12
|
|
|
