Solve a Linear Equation by Transposition Method

First let’s a review what is an equation. In mathematics, an equation is a mathematical expression where two sides of expression are connect to an “equality sign”.

In this tutorial we will learn how to solve a linear equation in one variable by transposition method. This method is as simple as Inverse Method.

In a linear equation, transpose is transferring a term from one side to the other side.

By solving the equation by changing its sign, the balance of equality of both sides of expressions is not affected. This is known as the process of transposition.

While solving the given linear equations we apply the linear equations rules.

To transpose a term from left hand side to right hand side or right hand side to left hand side, rules are as follows.

To solve the equation, change its sign and carry term to other side of the equation.

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1.Transpose ‘+’ sign of the term change to ‘-‘ sign to the other side.

2.Transpose ‘-‘ sign of the term change to ‘+’ sign to the other side.

3.Transpose ‘x’ sign of the term change to ‘÷’ sign to the other side.

4. Transpose ‘÷’ sign of the term change to ‘x’ sign to the other side.

To understand the linear equations in one variable by transposition method let’s start with examples.

For example: 2x + 6 = 8 is an algebraic equation.

(2x + 6) represents left hand side and 8 represents right hand side.

In transpose method, move from left hand side, over to right hand side, change it’s sign from plus(+) to minus(-).

In this equation 6 is added to 2x on LHS, so when we transpose 6 from LHS to RHS, we subtract 6

+6(LHS) ➡ -6(RHS)

So, the equation will be

2x = 8 – 6

2x = 2

Now 2x on LHS and 2 is coefficient of x so, when transpose 2 from LHS to RHS, we divide 2 in RHS by 2.

x = 2/2

2 Divide by 2 we get

x = 1

Check: 2x + 6 = 8

Put x =1 in LHS = 2 x 1 + 6

= 2 + 6

LHS = 8

RHS = 8

Both sides are equal to 8.

LHS = RHS

Hence checked.

Example: Solve the equation x + 5 = 9

Here, variable terms on one side and numbers on other side.

Transpose 5 from LHS to RHS

+5(LHS) ➡ -5(RHS)

We get, x = 9 – 5

x = 4

Check: x + 5 = 9,

put x = 4 in LHS

4 + 5 = 9

LHS = 9

RHS = 9

9 = 9, Both sides are equal.

LHS = RHS

Hence checked.

Example: x – 4 = 10

Here, 4 subtracted by x on one side we can transpose other side by add 4 to 10.

Then equation will be

x = 10 + 4

x = 14

Check: LHS = x – 4

= 14 – 4

LHS = 10

RHS = 10

10 = 10, Both sides are equal.

∴ LHS = RHS

Checked.

Example: 3x – 4 = 2x + 8

Step1: Transposing 4 from LHS to RHS

we get, 3x = 2x + 8 + 4

3x = 2x + 12

Step2: Transposing 2x from RHS to LHS

3x – 2x = 12

x = 12

Check: LHS = 3x – 4

= 3 x 12 – 4

= 36 – 4

LHS = 32

RHS = 2x + 8

= 2 x 12 + 8

= 24 + 8

= 32

32 = 32, Both sides are equal.

LHS = RHS

Hence checked.

Example: 3x = 18

To solve the given linear equation we apply the linear equations rules.

Step1: Transposing 3 from LHS to RHS

we get, x = 18/3

x = 6

Check: put x = 6 in LHS

3 x 6 = 18

LHS = 18

RHS = 18

Both sides are equal

LHS = RHS

Checked

Example: 3x/2 = 6

Transposing 2 from LHS to RHS

3x = 6 x 2

3x = 12

x = 12/3

x = 4

Example: 9x = 27

x = 27/9

x = 3

Check: Put x = 3 in given equation

9 x 3 = 27

LHS = 27,

RHS = 27

Both are equal

Hence checked