Arithmetic
Associative Property
Averages
Brackets
Closure Property
Commutative Property
Conversion of Measurement Units
Cube Root
Decimal
Divisibility Principles
Equality
Exponents
Factors
Fractions
Fundamental Operations
H.C.F / G.C.D
Integers
L.C.M
Multiples
Multiplicative Identity
Multiplicative Inverse
Numbers
Percentages
Profit and Loss
Ratio and Proportion
Simple Interest
Square Root
Unitary Method
Algebra
Algebraic Equation
Algebraic Expression
Cartesian System
Linear Equations
Order Relation
Polynomials
Probability
Standard Identities & their applications
Transpose
Geometry
Basic Geometrical Terms
Circle
Curves
Angles
Define Line, Line Segment and Rays
Non-Collinear Points
Parallelogram
Rectangle
Rhombus
Square
Three dimensional object
Trapezium
Triangle
Trigonometry
Trigonometry Ratios
Data-Handling
Arithmetic Mean
Frequency Distribution Table
Graphs
Median
Mode
Range
Home >> Linear Equations >> Linear Equation in one Variable >>

## Linear Equation in one Variable

 Linear Equations Complex Examples Linear Equation in one Variable Linear Equation in Two Variables Difference between Linear Equation in One & Two Variables Linear Expression

What are Linear Equations ?
What are Variables ?

What is Linear Equation in one variable

Linear equation is a equation in which there is only one variable and power of the variable is equals to 1 only.
e.g. 2x = 4, 3p + 1 = 5, a/10 -5 = 7, 3c + 12 = 7c all are examples of linear equation because:
2x = 4 ----- has one variable 'x' and power of the variable is 1
3p + 1 = 5 --------- has one variable 'p' and power of the variable is 1
a/10 -5 = 7 --------- has one variable 'a' and power of the variable is 1
3c + 12 = 7c --------- has one variable 'c' and power of the variable is 1

Let's try following some more examples:

Example 1: Is 2x + 4y = 5x is a linear expression
Solution: Given linear expression:
2x + 4y = 5

Variables in given linear expression:
x and y

Since, given equation have two variables i.e. x and y, so the given equation 2x + 4y = 5 is not a linear equation

Example 2: Is 9b2 - 12 = 34 is a linear expression
Solution: Given linear expression:
9b2 - 12 = 34

Variables in given linear expression is 'b', but power the variable b is 2, so given equation 9b2 - 12 = 34 is not a linear equation

Solving Linear Equation with one variable

Under this concept you will find the following solution:

• Linear Equation having Variables on one side and Natural Number on other side
Example: 2x + 5 = 15

• Linear Equation having Variable on both sides
Example: 2x + 11 = 3x

Let's understand above two situation in details:

Linear Equation having Variables on one side and Natural Number on other side

Example: 2x + 5 = 15
Solution: Given linear equation:
2x + 5 = 15

Subtract 5 from both sides and we get:
2x = 10

Divide both sides by 2 and we get:
x = 10

Hence, x = 10 is a solution to the given linear equation.

Linear Equation having Variable on both sides

Example: 2x + 11 = 3x
Solution: Given Linear equation:
2x + 11 = 3x

Subtract 11 from both sides and we get:
2x = 3x - 11

Transpose 3x to L.H.S and we get:
2x - 3x = (-11)

Solve subtraction on L.H.S and we get:
(-x) = (-11)

Divide both sides by (-1) and we get:
x = 11

Hence, x = 11 is a solution to the given linear equation.