Linear Equation in one Variable at Algebra Den

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Home >> Polynomials >> Linear Equations >> Linear Equation in one Variable >>

Linear Equation in one Variable

Linear Equation in one Variable Linear Equation in Two Variables Difference between Linear Equation in One & Two Variables Linear Expression Linear Equations Complex Examples
Solving a Pair of Linear Equations

Before you study this concept, you are adviced to read:

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.