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Objective: Now we will learn about finding the solution of a simple linear equation using the transposition method.

Transposition method:

Transposition method is one of the linear equation rules used to solve the linear equations.

In complicated equations, the two sides of an equation contain both variables and constants.

In complicated equations, the two sides of an equation contain both variables and constants.

In such cases, first, we should simplify the equation in simple forms.

And transpose the terms that contain variables on LHS and RHS.

That is in the transposition method the plus sign of the particular term changes into a minus sign on the other side and vice versa.

We can use the following steps to find a solution using transposition method:

Step 1) Identify the variables and constants in the given simple equation.

Step 2) Simplify the equation in \(LHS\) and \(RHS\).

Step 3) Transpose the term on the other side to solve the equation further simplest.

Step 4) Simplify the equation using arithmetic operation as required that is mentioned in rule \(1\) or rule \(2\) of linear equations.

Step 5) Then the result will be the solution for the given linear equation.

Important!

While transposing the terms sign changes inversely. If the terms sign is \((+)\) it will change as \((-)\) and vice versa.

Let's see an example to understand this method better.

Example:

Find the solution of $2x+14=32$

To solve the given linear equation we can use the linear equation rules. That is

**Step 1)**

**Transposing**14

**to RHS side.**

$\begin{array}{l}2x+14=32\\ \\ 2x=32-14\\ \\ 2x=18\end{array}$

**Step 2) Divide both sides by**2.

$\begin{array}{l}\frac{2x}{2}=\frac{18}{2}\\ \\ x\phantom{\rule{0.147em}{0ex}}=9\end{array}$

Thus the \(x =\) 9.

Therefore using this transposition rule we can find the solution for simple equations.

To check:

Though we find the solution for the simple equation. We also know that both LHS and RHS are equal.

Now let's learn how to check whether it is equal or not.

Consider the above example, we know the solution is \(x =\) 9.

Substitute this \(x\) value in the linear equation.

$\begin{array}{l}2x+14=32\\ \\ (2\times 9)+14=32\\ \\ 18\phantom{\rule{0.147em}{0ex}}+14=32\\ \\ 32=32\\ \\ \mathit{LHS}\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}\mathit{RHS}\end{array}$

Hence \(LHS = RHS\) so the solution we find is correct.

**Using this way we can find whether our solution is correct or not.**