Functions and More Functions - Beginning Pre-Calculus for Game Developers - page 92

Substituting the solution back into the original equation allows you test the
validity of your solution:

51
2

2

3 þ 4 ¼ 21

Substituting the solution :

102
2

1
3 þ 4 ¼ 21

Multiplying by 2 and dividing by 3 :

102
6 þ

24
6 ¼ 21

Finding a common denominator :

Canceling and clearing.

Here is one final example. You begin by clearing the fraction on the right side of
the equation. To accomplish this, you multiply both sides of the equation by the
value 6. This is a value you find in the denominator on the right side of the
equation. Having cleared the right side of the equation, you can then more easily
work to isolate the variable on the left side of the equation.

2 x
3 þ

4
3 ¼

5
6

Multiply by 6 to clear the fraction.

12 x
3 þ

24
3 ¼ 5

Carry out the multiplications :

12 x
3 þ

24
3 ¼ 5
4 x þ 8 ¼ 5

4 x þ 8 8 ¼ 5 8

:

Undo the addition

4 x

4 ¼ 3

Undo the multiplication :

4

3
4

x ¼