Solving for the Unknown - Basic Mathematics for Water and Wastewater Operators - page 116

■ Example 8.3
Problem : Solve for x , if 4 x - 4 = 8 (each side is in simplest terms).

Solution: Add +4 to each side of the equation to get

4 x = 8 + 4

4 x = 12

Now divide both sides:

4
4

x 12

4
3

=

x =

■ Example 8.4
Problem : Solve for x , if x + 10 = 15.

Solution: Subtract 10 from each member (axiom 2):

x = 15 - 10

Collect the terms:

x = 5

■ Example 8.5
Problem : Solve for x , if 5 x + 5 - 7 = 3 x + 6.

Solution: Collect the terms (+5) and (-7):

5 x - 2 = 3 x + 6

Add 2 to both members (axiom 2):

5 x = 3 x + 8

Subtract 3 x from both members (axiom 2):

2 x = 8

Divide both members by 2 (axiom 4):

x = 4