Functions and More Functions - Beginning Pre-Calculus for Game Developers - page 93

As with the previous examples, you can now substitute the solution back into the
original equation to test its validity.

2 x
3 þ

4
3 ¼

5
6

3
4

2

4
3 ¼

5
6

þ Substituting the solution :

3

4
3 ¼

5
6

6
4

3 þ

Multiplying by 2 :

4
3 ¼

5
6

3
2

3 þ

Simplifying :

3
2

1
3 þ

4
3 ¼

5
6

Dividing by 3 :

3
6 þ

4
3 ¼

5
6

Multiplying :

3
6 þ

4 ð 2 Þ
3 ð 2 Þ ¼

5
6

Finding the common denominator :

3
6 þ

8
6 ¼

5
6

Simplifying :

5
6 ¼

5
6

The solution is correct :

Exercise Set 5.4

a. x

2
7 ¼

4
6

3 þ

b. 4x

1
5 ¼

4
20 2 þ

c. 4x

6
3 ¼

4
6

3 þ

d. 6b
2

2
8 ¼

2
4

4