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.

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

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.