Equation: A statement of equality of two algebraic expressions involving one or more variables is called an equation.

Linear Equation: An equation of degree 1 containing one or more variables, is called a linear equation.

Simple Linear Equations (Linear Equations in One Variable): An equation of degree 1 containing only one variable is called a simple linear equation.

Some examples of simple linear equations are:

Example:

Mathematically, an equation which can be expressed in the form

is called a simple linear equation in the variable *x*. This is also called the standard form of a simple linear equation.

Solution (or Root) of an Equation: Any value of the variable which when substituted in an equation makes its left hand side (L.H.S) equal to its right hand side (R.H.S.) is called a solution (or root) of the equation.

Thus, is a root of the equation

Therefore, solving an equation means finding all its solutions (or roots).

*Note: In a simple linear equation, there is one solution for the variable. We will see that in equations of higher degree, there is more than one solution (root).*

Basics rules that apply to equations:

- Same number (or expression) can be added to both sides of an equation without altering the solution.
- Same number (or expression) can be subtracted from both sides of an equation without altering the solution.
- Both sides of an equation can be multiplied by the same non-zero number (or expression) without altering the solution.
- Both sides of an equation can be divided by the same non-zero number (or expression) without altering the solution.

Transposition: Any term of an equation may be taken to the other side with the sign changed. This process is called transposition.

Example

or

or

Cross Multiplication:

This process is called cross multiplication.

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