# 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

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.

## Recent Articles

1. ### 4th Grade Mental Math on Roman Numerals | Roman Numerals Quiz

Feb 23, 24 03:55 PM

In 4th grade mental math on numbers, students can practice different questions on write the Hindu-Arabic numerals, write the Roman Numerals, comparison of roman numerals, addition of roman numerals.

Feb 23, 24 02:24 PM

In 4th grade mental math on numbers, students can practice different questions on numbers in figures, number name, place value, face value, comparison of number and formation of greatest and smallest…

3. ### Roman Numerals | System of Numbers | Symbol of Roman Numerals |Numbers

Feb 23, 24 01:28 PM

How to read and write roman numerals? Hundreds of year ago, the Romans had a system of numbers which had only seven symbols. Each symbol had a different value and there was no symbol for 0. The symbol…

4. ### Worksheet on Roman Numerals |Roman Numerals|Symbols for Roman Numerals

Feb 22, 24 04:15 PM

Practice the worksheet on roman numerals or numbers. This sheet will encourage the students to practice about the symbols for roman numerals and their values. Write the number for the following: (a) V…