Balancing Method

Solving an equation means finding the value of the unknown, which makes the equation true.

To use the balancing method to solve a simple equation, add, subtract, divide or multiply both sides of the equation with the same quantity. In other words, whatever operation is done to one side of the equation needs to also be done to the other.

Example 6.1.1:

Solve the following equation using the balancing method:

a.  \( \scriptsize x \: + \: 8 \: = \: 19\)

b. \( \scriptsize x \: – \: 20 \: = \: 35\)

c. \( \scriptsize 3x \: = \: 27\)

d. \( \scriptsize 3x \: – \: 7 \: = \: 8\)

e. \( \frac{x}{6} \scriptsize \: = \: 7\)

Solution 

a.  \( \scriptsize x \: + \: 8 \: = \: 19\)

Additive inverse of +8 = -8 

We are going to add (-8) to both sides

\( \scriptsize x \: + \: 8 \: + \: (-8) \: = \: 19 \: + \: (-8) \\ \scriptsize x \: + \: 8 \: – \: 8 \: = \: 19 \: – \: 8 \\ \scriptsize x \: + \: 0 \: = \: 19 \: – \: 8 \\ \scriptsize x \: = \: 19 \: – \: 8 \\ \scriptsize x \: = \: 11 \)