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Variables: - In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

In $\frac{x}{2}+1=\frac{1}{4}x鈭�6$, x is the variable which is the unknown quantity.

Constants: - In any expression or equation constant are the values which is fixed.

Here, 1 and 6 are constants.

Also, $\frac{x}{2}$ and $\frac{1}{4}x$ are the product of a constant and variable.

While performing addition in an equation, the same kind of elements or like terms are added together.

In the given equation, terms with the variable x will be added all together and while performing addition constant terms which are multiplied with the variables are added.

$\frac{x}{2}+1=\frac{1}{4}x鈭�6$

Add $鈭�\frac{1}{4}x鈭�1$ both sides of the equation and simplify.

$\begin{array}{l}\frac{x}{2}+1鈭�\frac{1}{4}x鈭�1=\frac{1}{4}x鈭�6鈭�\frac{1}{4}x鈭�1\\ \frac{x}{2}鈭�\frac{1}{4}x+1鈭�1=\frac{1}{4}x鈭�\frac{1}{4}x鈭�6鈭�1\\ \frac{2x鈭�x}{4}+0=0鈭�6鈭�1\\ \frac{x}{4}=鈭�7\end{array}$

Multiply both the sides by 4 and simplify.

$\begin{array}{l}\frac{x}{4}脳4=鈭�7脳4\\ x=鈭�28\end{array}$

Hence on solving $\frac{x}{2}+1=\frac{1}{4}x鈭�6$ the obtained value of x is $鈭�28$.

Put $x=鈭�28$ in $\frac{x}{2}+1=\frac{1}{4}x鈭�6$ and check whether the value on the right-hand side is equal to the value on the left-hand side.

$\frac{\left(鈭�28\right)}{2}+1=\frac{1}{4}\left(鈭�28\right)鈭�6$

First, evaluate the value on the left-hand side.

$\begin{array}{c}\frac{\left(鈭�28\right)}{2}+1=\frac{鈭�28+2\left(1\right)}{2}\\ =\frac{鈭�28+2}{2}\\ =鈭�\frac{26}{2}\\ =鈭�13\end{array}$

Now, evaluate the values of right- hand side, that is, $\frac{1}{4}\left(鈭�28\right)鈭�6$.

$\begin{array}{c}\frac{1}{4}\left(鈭�28\right)鈭�6=\frac{鈭�28鈭�6\left(4\right)}{4}\\ =\frac{鈭�28鈭�24}{4}\\ =\frac{鈭�52}{4}\\ =鈭�13\end{array}$

Since the values of both sides are equal, the obtained result is true and verified.