### Theory:

Solution of an equation:
A solution of an equation is a number substituted for an unknown variable which makes the equality in the equation true.
Example:
Consider the equation $$2x + 3 = 7$$. Solve the equation.

We know that the equality shows that the unknown variable makes the equation true. That is, when the variable $$x = 2$$, we can see that the LHS and RHS are same. Hence, $$x = 2$$ is the solution of the given equation.
1. The DO - UNDO method:

Let us understand the concept with an example.
Find the solution for $$2$$ times $$x$$ is more than $$3$$ equals $$7$$.

Solution:

First, let us frame the equation.

$$2x + 3 = 7$$

We have framed the equation from $$x$$. To determine the value of $$x$$, we need to undo what we did to arrive at the solution. Hence, we do to frame the equation and undo to find the solution.

Now, let us undo the equation.

$$2x +3 - 3 = 7 - 3$$ (Subtract $$3$$ from both sides)

$$2x = 4$$ (Simplify)

$$\frac{2x}{2}=\frac{4}{2}$$ (Divide by $$2$$ on both sides)

$$x = 2$$ (Simplify)

Therefore, $$x = 2$$ is the solution of the equation.
2. Transposition method:
Transferring the number from one side to the other side of the equation is called a transposition method.
Example:
1. Solve the equation $$2x + 3 = 7$$ using transposition method.

Solution:

Transfer the number $$3$$ to the other side of the equation and changing its sign.

Thus, we have:

$$2x = 7 - 3$$

$$2x = 4$$

Now, instead of dividing both sides of the equation by $$2$$, let us transfer the number $$2$$ to the other side of the equation and reciprocating, we get:

$$x = \frac{4}{2}$$

$$x = 2$$

Thus, the solution of the equation is $$2$$.

2. Find the solution of $$\frac{x}{2} - 1 = 13$$.

Solution:

Transfer the number $$1$$ to the other side of the equation and changing its sign.

Thus, we have:

$$\frac{x}{2} = 13 + 1$$

$$\frac{x}{2} = 14$$

Now, transfer $$2$$ to the RHS and reciprocate the number. Then, we have:

$$x = 14 \times 2$$

$$x = 28$$

Thus, the solution is $$x = 28$$.