Linear Equation

What is a linear equation?

An equation which involves only one variable whose highest power is 1 is known as a linear equation in that variable.

For example:

(a) x + 4 = 19 

(b) y - 7 = 11 

(c) x/2 - x/3 = 9 

(d) 2x - 5 = x + 7

(e) x + 13 = 27 

(f) y - 3 = 9 

(g) 11x + 5 = x + 7

Each one of these equations is a linear equation. 


The sign of equality divides the equation into two sides. Left hand side or L.H.S. and Right hand side or R.H.S


Solution of linear equation or Root of linear equation: The value of the variable which makes left hand side equal to right hand side in the given equation is called the solution or the root of the equation.

For example:

1. x + 1 = 4

Here, L.H.S. is x + 1 and R.H.S. is 4

If we put x = 3, then L.H.S. is 3 + 1 which is equal to R.H.S.

Thus, the solution of the given linear equation is x = 3


2. 5x - 2 = 3x - 4 is a linear equation.

If we put x = -1, then L.H.S. is 5 × -1 -2 and R.H.S. is 3 × -1 -4

                                            = -5 -2                           = -3 -4

                                            = -7                               = -7

So, L.H.S. = R.H.S.

Therefore, x = -1 is the solution for the equation 5x - 2 = 3x - 4

How to solve linear equation in one variable?

Rules for solving a linear equation in one variable: 

The equation remains unchanged if – 

(a)The same number is added to both sides of the equation.

For example: 

1. x - 4 = 7 

⇒ x - 4 + 4 = 7 + 4 (Add 4 to both sides) 

⇒ x = 11 


2. x - 2 = 10

⇒ x - 2 + 2 = 10 + 2 (Add 2 to both sides)

⇒ x = 12 



(b) The same number is subtracted from both sides of the equation.

For example:

1. x + 5 = 9

⇒ x + 5 - 5 = 9 - 5 (Subtract 5 from both sides)

⇒ x + 0 = 4

⇒ x = 4


2. x + 1/2 = 3

x + 1/2 - 1/2 = 3 - 1/2 (Subtract 1/2 from both sides)

⇒ x = 3 - 1/2

⇒ x = (6 - 1)/2

⇒ x = 5/2



(c) The same number is multiplied to both sides of the equation.

For example:

1. x/2 = 5

⇒ x/2 × 2 = 5 × 2 (Multiply 2 to both the sides)

⇒ x = 10


2. x/5 = 15

⇒ x/5 × 5 = 15/5 (Multiply 5 to both the sides)

⇒ x = 3



(d) The same non-zero number divides both sides of the equation.

For example:

1. 0.2x = 0.24

⇒ 0.2x/0.2 = 0.24/0.2 (Divide both sides by 0.2)

⇒ x = 0.12


2. 5x = 10

⇒ 5x/5 = 10/5 (Divide both sides by 2)

⇒ x = 2

What is transposition? Explain the methods of transposition.

Any term of an equation may be shifted to the other side with a change in its sign without affecting the equality. This process is called transposition.

So, by transposing a term —

We simply change its sign and carry it to the other side of the equation.

‘+‘ sign of the term changes to ‘—‘ sign to the other side and vice-versa.

‘×’ sign of the factor changes to ‘÷‘ sign to the other side and vice-versa.

Now, simplify L.H.S. such that each side contains just one term.

Finally, simplify the equation to get the value of the variable.

For example:

10x - 7 = 8x + 13

⇒ 10x - 8x = 13 + 7

⇒ 2x = 20

⇒ 2x/2 = 20/2

⇒ x = 10

Note:

    + changes to –

    – changes to +

    × changes to ÷

    ÷ changes to ×

Therefore, from the above we came to know that without changing the equality, this process of changing sign is called transposition.


 Equations

What is an Equation?

What is a Linear Equation?

How to Solve Linear Equations?

Solving Linear Equations

Problems on Linear Equations in One Variable

Word Problems on Linear Equations in One Variable

Practice Test on Linear Equations

Practice Test on Word Problems on Linear Equations


 Equations - Worksheets

Worksheet on Linear Equations

Worksheet on Word Problems on Linear Equation









7th Grade Math Problems 

8th Grade Math Practice 

From Linear Equation to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Converting Fractions to Decimals | Solved Examples | Free Worksheet

    Apr 28, 25 01:43 AM

    Converting Fractions to Decimals
    In converting fractions to decimals, we know that decimals are fractions with denominators 10, 100, 1000 etc. In order to convert other fractions into decimals, we follow the following steps:

    Read More

  2. Expanded Form of a Number | Writing Numbers in Expanded Form | Values

    Apr 27, 25 10:13 AM

    Expanded Form of a Number
    We know that the number written as sum of the place-values of its digits is called the expanded form of a number. In expanded form of a number, the number is shown according to the place values of its…

    Read More

  3. Converting Decimals to Fractions | Solved Examples | Free Worksheet

    Apr 26, 25 04:56 PM

    Converting Decimals to Fractions
    In converting decimals to fractions, we know that a decimal can always be converted into a fraction by using the following steps: Step I: Obtain the decimal. Step II: Remove the decimal points from th…

    Read More

  4. Worksheet on Decimal Numbers | Decimals Number Concepts | Answers

    Apr 26, 25 03:48 PM

    Worksheet on Decimal Numbers
    Practice different types of math questions given in the worksheet on decimal numbers, these math problems will help the students to review decimals number concepts.

    Read More

  5. Multiplication Table of 4 |Read and Write the Table of 4|4 Times Table

    Apr 26, 25 01:00 PM

    Multiplication Table of Four
    Repeated addition by 4’s means the multiplication table of 4. (i) When 5 candle-stands having four candles each. By repeated addition we can show 4 + 4 + 4 + 4 + 4 = 20 Then, four 5 times

    Read More