Linear Equation in One Variable

 Linear Equation in One Variable 

Notes & NCERT SOLUTIONS 

 Equation (in Mathematics)

Definition:

An equation is a mathematical statement that shows the equality of two algebraic expressions using the symbol “=”.

 Example:


2x + 3 = 7

Here:

Left side → Left Hand Side (LHS)


Right side → Right Hand Side (RHS)

An equation is true only for certain values of the variable.

These values are called solutions of the equation.


Algebraic Expression

An algebraic expression is a combination of variables, constants, and arithmetic operations (+, −, ×, ÷) without an equality sign.

 Examples:

 Expressions do not show equality, so they cannot be solved, only simplified.



 Variable

A variable is a symbol (usually a letter like ) that represents an unknown or changeable quantity which depends on Mathematical Situations and conditions.

 Example:

In , x+3

x is the variable.

 A variable can take different numerical values.


 Constant

A constant is a number with a fixed value that does not change.

 Examples:

In , x+3


3 is a constant.


 Coefficient

The coefficient is the numerical factor multiplied with a variable.

 Examples:


In , 7x +3 coefficient of x is 7


In , x-3/2y =7 coefficient of y is −3/2



Note:  If no number is written before a variable, the coefficient is 1.


 Degree (of an Expression)

The degree of an algebraic expression is the highest power of the variable present in it.


👉 Examples:


 x+3→ degree 1


x² +4x → degree 2


 Linear Expression

A linear expression is an algebraic expression in which the highest power of the variable is 1.

 Examples: x+5, 

 y+ 3x =3

9 - 9x = 7


Not linear:

x + 1/x = 3


 Linear Equation


A linear equation is an equation in which the highest power of the variable is 1.

 Standard form:

ax + b = 0

a, b are real numbers

 Example:


3x - 6 = 0



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