Solving linear equations

The process of finding the value of the unknown quantity for which the equation is true, is called solving the equation. The value so found is called the root or solution of the equation.The process of finding the value of the unknown quantity for which the equation is true, is called solving the equation. The value so found is called the root or solution of the equation.

The process of solving a simple equation depends upon the following axioms:

Addition property

If any number is added to both sides of an equation, then the equality of the equation remains unchanged.

i.e., if x = y then x + a = y + a

Subtraction property

If any number is subtracted from both sides of an equation, then the equality of the equation remains unchanged.

i.e., if x = y, then x - a = y - a

Multiplication and division property

The following are also true.

where a is a non-zero constant.

Example 1:

x + 3 = 4

x + 3 - 3 = 4 - 3 [- 3 is added to both sides of the equation]

Example 2:

2x = 16