Math Doubts

Solving Linear Equations in One Variable by Transposition

A method of transferring a term in a linear equation from one side to other side by changing its sign for solving it, is called solving linear equation in one variable by transposition method.

Introduction

According to English language, the meaning of transpose is, transfer a term to the other side of an equation by changing its sign.

In transposition method, a term is transposed to the other side of an equation with its sign changed. It balances the equality of both expressions and also simplifies the linear equation in one variable. Thus, the root of the linear equation in one variable can be calculated easily in mathematics.

Examples

$(1) \,\,\,\,\,\,$ $x-3 = 5$

In this linear equation in one variable, $x$ and $3$ are two terms in the left-hand side of the equation. If the term $3$ is transferred to other side of the equation, then it is easy to find the solution of this equation but the sign of the term $3$ is negative. So, it can be shifted to other side by changing its sign.

$\implies$ $x = 5+3$

$\,\,\, \therefore \,\,\,\,\,\,$ $x = 8$

$(2) \,\,\,\,\,\,$ $2x = 12+x$

It is another example for linear equation in one variable. In this linear equation, $12$ and $x$ are two terms in the right-hand side of the equation. The linear equation can be solved by transposing the term $x$ to left-hand side of the equation from right-hand side by changing its sign.

$\implies$ $2x-x = 12$

$\implies$ $(2-1)x = 12$

$\,\,\, \therefore \,\,\,\,\,\,$ $x = 12$

In this way, the terms are transposed in a linear equation in transposing method for solving linear equations in one variable.



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