### Theory:

**Objective:**

In this chapter, we will study to solve an equation if the equation contains a variable on both sides.

**Solving a linear equation with the variable on both sides:**

We already studied to solve a linear equation with a single variable. Now we will look into how to solve an equation if it consists of variable in both sides.

**For example:**

**Solve:**$2x+6=x+14$

This linear equation consists of the variable on both sides.

\(LHS =\) $2x+6$.

\(RHS =\) $x-14$.

Now we see a couple of steps to solve the equation.

**Step I)**

The equation is $2x+6=x+14$.

Now transpose the 6 to \(RHS\) side and transpose the variable \(x\) in \(RHS\) to \(LHS\) respect to the given equation.

Now transpose the 6 to \(RHS\) side and transpose the variable \(x\) in \(RHS\) to \(LHS\) respect to the given equation.

$\begin{array}{l}2x-x=14-6\\ \\ 1x=8\end{array}$

**Step II)**

Divide by 1 on both side.

$\begin{array}{l}1x=8\\ \\ \frac{1x}{1}=\frac{8}{1}\\ \\ x\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}8\end{array}$

From the above steps, we observed that we could transpose the constant and the variable to either side of the equation as per required.

**Let's summarize what we have learned here:**

Steps to solve on linear equation with the variable on both sides:

**1.**Observe the given linear equation.

**2.**Transpose the constant and variable term to \(LHS\) and \(RHS\) respect to the given linear equation.

**3.**Divide by the coefficient of the variable on both sides.

**4.**Then we get the solution of the given linear equation.